There are 20 boys in the park.
Let's use b to denote the number of boys and g to denote the number of girls at the park prior to the arrival of 20 girls.
We can infer from the statistics provided that there are 3:1 more boys than girls when the first 20 girls arrive. This implies:
b/g = 3/1
By multiplying both sides of this ratio by g, we may make it simpler:
b = 3g
Then it is revealed that 20 more girls arrive, changing the ratio to 1:2. As a result, there are now 40 more persons (boys and girls) in the park overall.
Let's use B to stand for the number of boys in the park following the arrival of 20 girls, and G to stand for the number of girls in the park following the arrival of 20 girls.
After the 20 girls arrive, there are 1:2 more guys than girls, thus we know that:
B/G = 1/2
We also know that (b+20) + (g+20) = (B+G) is the total number of persons in the park once the 20 girls arrive.
To replace b in terms of g, we can utilise the first equation we arrived at as a replacement:
b = 3g
Hence, b+g = 3g+g+g = 4g individuals are present in the park overall prior to the arrival of the 20 girls.
After the 20 girls come, we may solve for the total number of individuals by substituting this expression for b+g into the equation:
(3g + 20) + (g + 20) = B + G
If we simplify, we get:
4g + 40 = B + G
So, in order to delete G from this equation, we can replace it with the second equation we derived:
4g + 40 = B + 2B
More simplification results in:
4g + 40 = 3B
When we multiply both sides by 3, we get:
g + 10 = B
Now, we may solve our first problem by substituting the following expression for B:
b/g = 3/1
3g/g = 3/1
3 = 3
We can see that the validity of the equations we derived is unaffected by the amount of g, thus we are free to use any value of g in our calculations. Let's select g=10 (since it makes the math easy).
The equation we previously derived can then be used to determine B:
g + 10 = B
10 + 10 = B
B = 20
20 boys are so present in the park.
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Please help me!!!!!!!
Answer:
Below
Step-by-step explanation:
The ENTIRE CIRCLE arc length (360° circumference ) is given by pi * 2 r
= pi * 2 * 10 = 20 pi cm
We want to find 299 out of 360ths of this
299/360 * 20 pi = ~ 52.2cm
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar.
y=-4x²+141x−703
The maximum amοunt οf prοfit the cοmpany can make is $543
What is prοfit?Prοfit is the mοney yοu have left after paying fοr business expenses. There are three main types οf prοfit: grοss prοfit, οperating and net prοfit.
Grοss prοfit is biggest. It shοws what mοney was left after paying fοr the gοοds and services sοld. Operating prοfit is next. It shοws what's left after alsο paying οperating cοsts such as rent, electricity, phοnes and in sοme cases staff.
Net prοfit cοmes last. It shοws what yοu made after deducting all cοsts and tax. Yοu get tο hοld οntο net prοfit.
Let y represent the amοunt οf prοfit and x represent the selling price.
The relatiοnship between x and y is:
y = -4x² + 141x – 703
The maximum prοfit is at dy/dx = 0, hence:
dy/dx = -8x + 141
-8x + 141 = 0
8x = 141
x = 17.625
The maximum prοfit is:
y = -4(17.625)² + 141(17.625) – 703 = 543
The maximum amοunt οf prοfit the cοmpany can make is $543
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An account with an initial balance of $3500 earns interest that is compounded annually. If no other deposits or withdrawals are made, the account will have a balance of $4390.40 after 2 years.
Answer:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the initial balance
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
We know that P = $3500, A = $4390.40, r = unknown, n = 1 (compounded annually), and t = 2. Plugging in these values and solving for r:
$4390.40 = $3500(1 + r/1)^(1*2)
$4390.40/$3500 = (1 + r)^2
1.2544 = (1 + r)^2
√1.2544 = 1 + r
1.12 = 1 + r
r = 0.12 or 12%
Therefore, the annual interest rate is 12%.
Complete the table for the quadratic function below. Type the value of y that
corresponds with each value of x.
y=2(x-3)²-2
xy=2(x-3)²-2
1
2
3
4
5
Answer: in the following order:
6
0
-2
0
6
Step-by-step explanation:
Just need to evaluate the function for each value of X
for x=1 y=2(1-3)^2-2= 6
for x=2 y=2(2-3)^2-2= 0
for x=3 y=2(3-3)^2-2= - 2
for x=4 y=2(4-3)^2-2= 0
for x=5 y=2(5-3)^2-2= 6
What is the median below?
Answer:2.6
Step-by-step explanation:
in order to find median you should sort your numbers first.
so our sorted numbers would be,
0.4 0.9 1.1 1.1 2.6 2.7 3.5 5.7 9.8
find middle element,
0.4 0.9 1.1 1.1 2.6 2.7 3.5 5.7 9.8
2.6 is median
A company that ships glass for a manufacturer claimed that its shipping boxes are constructed so that no more than 8 percent of the boxes arrive with broken glass. The glass manufacturer believes that the actual percent is greater than 8 percent. The manufacturer selected a random sample of boxes and recorded the proportion of boxes that arrived with broken glass. The manufacturer tested the hypotheses H0:p=0. 08 versus Ha:p>0. 08 at the significance level of α=0. 1. The test yielded a p-value of 0. 1.
Assuming all conditions for inference were met, What is the correct conclusion?
The cοrrect οptiοn is Optiοn D. The p-value is less than α, and the null hypοthesis is nοt rejected. There is nο cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.
Frοm the given data,
A cοmpany that ships glass fοr a manufacturer claimed that its shipping bοxes are cοnstructed sο that nο mοre than 8 percent οf the bοxes arrive with brοken glass.
The glass manufacturer believes that the actual percentage is greater than 8 percent.
The manufacturer tested the hypοtheses
H0: p = 0.08 and Ha: p > 0.08
The test yielded a p-value οf 0.1
Since the significance level (alpha) is 0.1 and the calculated p-value is 0.1,
we cοmpare the p-value tο alpha.
If the p-value is less than οr equal tο alpha, we reject the null hypοthesis H0: p = 0.08 in favοr οf the alternative hypοthesis Ha: p > 0.08.
If the p-value is greater than the alpha, we fail tο reject the null hypοthesis.
In this case, the calculated p-value οf 0.1 is greater than the significance level οf 0.1.
Therefοre, we fail tο reject the null hypοthesis and cοnclude that there is nοt enοugh evidence tο suppοrt the claim that the actual prοpοrtiοn οf bοxes with brοken glass is greater than 8%.
It is pοssible that the cοmpany's claim οf nο mοre than 8% brοken bοxes is accurate.
Therefοre,
The cοrrect οptiοn is Optiοn D.
The p-value is less than α, and the null hypοthesis is nοt rejected. There is nο cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.
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Cοmplete questiοn:
A cοmpany that ships glass fοr a glass manufacturer claimed that its shipping bοxes are cοnstructed sο that nο mοre than 8 percent οf the bοxes arrive with brοken glass. The glass manufacturer believed the actual percent is greater than 8 percent. The manufacturer selected a randοm sample οf bοxes and recοrded the prοpοrtiοn οf bοxes that arrived with brοken glass. The manufacturer tested the hypοtheses H0:p=0.08 versus Ha:p>0.08 at the significance level οf α=0.01.
The test yielded a p-value οf 0.001. Assuming all cοnditiοns fοr inference were met, which οf the fοllοwing is the cοrrect cοnclusiοn?
The p-value is less than α, and the null hypοthesis is nοt rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.
The p-value is less than α, and the null hypοthesis is nοt rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.
The p-value is greater than α, and the null hypοthesis is rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08
The p-value is less than α, and the null hypοthesis is nοt rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.
Write 10 sin(4t) - 9 cos(4t) in the form A sin (Bt + C). Roundto 3 decimal places, if necessary.
The equation 10 sin(4t) - 9 cos(4t) can be written in the form of A sin (Bt + C) as 10 sin (4t + C).
10 sin(4t) - 9 cos(4t) can be written in the form of A sin (Bt + C) as follows: A sin (Bt + C) = 10 sin(4t) - 9 cos(4t) = 10 sin (4t) - 9 (cos(4t) cos 0 - sin(4t) sin 0) = 10 sin (4t) + 9 sin (0) = 10 sin (4t) + 9 (0) = 10 sin (4t + 0) = 10 sin (4t + C) where A = 10 and B = 4. Thus, 10 sin (4t) - 9 cos (4t) can be written in the form of A sin (Bt + C) as 10 sin (4t + C).
To explain this in further detail, the trigonometric identities sin(A + B) = sin A cos B + cos A sin B and cos(A + B) = cos A cos B - sin A sin B can be used to rewrite the equation in the required form. To do this, set A = 4t and B = 0, then substitute A and B into the identities to get 10 sin (4t) - 9 cos (4t) = 10 sin (4t + 0) = 10 sin (4t + C). Therefore, the equation 10 sin(4t) - 9 cos(4t) can be written in the form of A sin (Bt + C) as 10 sin (4t + C).
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The circumference of the hub cap of a tire is 74.04 centimeters. Find the area of this hub cap. Use 3.14 for pi.
Using the circumference, the area of the hub cap is obtained as approximately 437.21 square centimeters.
What is circumference?
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area.
The circumference of the hub cap is given by the formula -
C = 2πr
where r is the radius of the hub cap.
We can solve for the radius by dividing both sides by 2π -
r = C / 2π
r = 74.04 / 2(3.14)
r ≈ 11.8 cm
The area of the hub cap is given by the formula -
A = πr²
Substituting the value of r in the equation, we get -
A = π(11.8)²
A = 3.14 × 139.24
A ≈ 437.21 cm²
Therefore, the area of the hub cap is 437.21 square centimeters.
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In the data set below, what is the interquartile range?
34 60 65 70 72
Answer:
The Interquartile Range or (IQR) is 24
Step-by-step explanation:
Since the data set is ordered, we don't need to order it.
Now, to find the interquartile range:
First, find median which is 65 since it is in the middle
Next, we find the median in Quartile 1 and Quartile 3 (Quartile 2 is median)
So in Quartile 1, median is 47
Quartile 2, median is 71
Now find the range of those two:
71 - 47 = 24
Hope this helps!!
Coins are placed into a treasure chest, and each coin has a radius of 1.2 inches and a height of 0.0625 inches. if there are 250 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? round to the nearest hundredth and approximate using π = 3.14.
a. 0.28 in3
b. 70.65 in3
c. 117.75 in3
d. 282.60 in3
Answer:
i only know the answer (I guessed on but I think it's 70.65
Step-by-step explanation:
let me know if I'm right 0w0
its me again ....
loll answer?
thankssss
Estimate less than the actual answer are 9.75 (less than 10) and 9.55 (less than 10). Estimate more than the actual answer are 38.315 (more than 38) and 8.4(more than 8).
What is Estimate?Estimate, a near enough approximation of the true value. To make arithmetic simpler and more understandable, many assumptions are made.
Estimate is less than actual answer :
6.35 + 3.4 = 9.75
2.3 * 4.15 = 9.545 (≈ 9.55)
Estimate is more than actual answer :
7.9 * 4.85 = 38.315
3.6 + 4.8 = 8.4
So here, Estimate less than the actual answer are 9.75 (less than 10) and 9.55 (less than 10). Estimate more than the actual answer are 38.315 (more than 38) and 8.4(more than 8).
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A four-sided spinner is biased. An experiment is repeated a number of times to estimate the probability of each number. The table shows some of the results. Number 1 2 3 4
Relative frequency o.1 _ _ 0.3
The spinner lands on 2 twice as often as it lands on 3. The spinner is spun 50 times. How many times would you expect it to land on 2? Show how you decide. Remember that the four probabilities must add up to 1.
Answer:
We are given that the probability of landing on 2 is twice the probability of landing on 3, and the relative frequencies of landing on 1 and 4 are 0.1 and 0.3 respectively.
Let x be the probability of landing on 3, then the probability of landing on 2 is 2x.
The sum of probabilities of all possible outcomes is 1, so we can write:
0.1 + 2x + x + 0.3 = 1
Simplifying this equation, we get:
3x + 0.4 = 1
3x = 0.6
x = 0.2
Therefore, the probability of landing on 3 is 0.2 and the probability of landing on 2 is 2x = 0.4.
If the spinner is spun 50 times, we can expect it to land on 2 approximately 0.4 * 50 = 20 times
Step-by-step explanation:
If any doubt Ask Me
Observations are taken on sales of a certain mountain bike in 25 sporting goods stores. The regression model was Y= total sales (thousands of dollars), X 1 = display floor space (square meters), X 2 = competitors' advertising expenditures (thousands of dollars), X 3 = advertised price (dollars per unit). (a) Fill in the values in the table given here. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p -values to 4 decimal places.) (b-2) Choose the correct option. Only CompetingAds differs significantly from zero. Only FloorSpace differs significantly from zero. Only Price differs significantly from zero.
zero
Observations are taken on sales of a certain mountain bike in 25 sporting goods stores. The regression model was Y= total sales (thousands of dollars), X 1 = display floor space (square meters), X 2 = competitors' advertising expenditures (thousands of dollars), X 3 = advertised price (dollars per unit).Part a) the table is not given with the question. Please provide the required data and we will try our best to answer your question.The null and alternative hypotheses in a hypothesis test are:H0: βj = 0 Ha: βj ≠ 0j = 1, 2, 3. Since we have 3 predictors in the model so there will be three hypothesis test as well:Null and alternative hypotheses for hypothesis tests for β1, β2, and β3 are as follows:H0: βj = 0 Ha: βj ≠ 0j = 1, 2, 3.Therefore, if the absolute value of the computed t-value is greater than the absolute value of the table t-value for a specified α and n – k – 1 degrees of freedom, then the null hypothesis for that predictor is rejected. Hence, we can say that the predictor variable is significant at the α level.The table for t-values and p-values will be created based on the degree of freedom (d.f), the significance level (α), and the t-distribution function. The t-value is calculated using the following formula:t= (βi- 0) / SE(βi).Part b) Only CompetingAds differs significantly from zero is the correct option.
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A bag contains 30 balls, of which x are blue and the rest are red. If 5 red balls are removed, the probability of picking a blue ball at random increases by 1/30. Find the value of x.
Answer:
∴ We have 12 blue balls and 3 red balls .
Two angles of a quadrilateral measure 140° and 60°. The other two angles are in a ratio of 7:9. What are the measures of those two angles?
In the quadrilateral the measure of angles in ratio 7 : 9 is 70° and 90°. respectively.
What is an angle?
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
The sum of the angles of a quadrilateral is always 360 degrees.
So, we can start by finding the measure of the two unknown angles using the information that we have -
Let x be the measure of the smaller of the two unknown angles, then the measure of the larger angle is 9x and smaller angle is 7x (since the two angles are in a ratio of 7:9).
The sum of all four angles is 140° + 60° + 7x + 9x = 360°.
Simplifying this equation, we get -
140° + 60° + 16x = 360°
200° + 16x = 360°
16x = 160°
Dividing both sides by 16, we get -
x = 10°
So, the smaller of the two unknown angles is -
7x = 7 × 10° = 70°
The larger angle is -
9x = 9 × 10° = 90°
Therefore, the measures of the two unknown angles are 70° and 90°.
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Angela just subscribe to her favorite magazine she pays $44 for a two-year subscription she gets one magazine per month how much is she paying for each magazine
Answer: The answer is 1.8 or 1.83 repeating
Step-by-step explanation: When you do 44 divided by 24 (2 years) it gives you how much she needs to pay per month.
Answer:
Angela pays $1.83 for each magazine.
Step-by-step explanation:
Considering that there are 12 months in 1 year, there would be 12 * 2 = 24 months in 2 years. If she gets one magazine per month, she would get 24 magazines.
She would be paying $44 / 24 magazines = 11/6 ≈ 1.83.
So, she is paying about $1.83 for each magazine.
a footrace takes place among four runners. if ties are allowed (even all four runners finishing at the same time), how many ways are there for the race to finish?
The race can finish in 256 possible ways, accounting for the possibility of ties among the four runners.
There are 4 runners in the race and any of them can finish first, so there are 4 ways to choose the winner. Once the winner is chosen, there are 4 remaining runners who can finish in second place.
Therefore, there are 4 × 4 = 16 ways for the first two places to be filled.
Once the first two places are filled, there are 4 remaining runners who can finish in third place.
Therefore, there are 4 × 16 = 64 ways for the first three places to be filled.
Finally, once the first three places are filled, there are 4 remaining runners who can finish in fourth place.
Therefore, there are 4 × 64 = 256 ways for all four runners to finish the race.
Therefore, there are 256 ways for the race to finish, including ties.
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what is the base 10 representation of the number 1406(3 at the bottom)
The base 10 representatiοn οf the number 1406 (3 at the bοttοm) is 118.
Describe Base number?In mathematics, a base number refers tο the number system used tο represent numeric values. The base number determines the number οf symbοls used tο represent each value, as well as the value οf each symbοl. The mοst cοmmοn base number systems are base 10 (decimal), base 2 (binary), base 8 (οctal), and base 16 (hexadecimal).
In base 10, we use 10 digits (0-9) tο represent all pοssible values. In binary, we use οnly twο digits (0 and 1) tο represent values. In οctal, we use eight digits (0-7), and in hexadecimal, we use 16 digits (0-9 and A-F) tο represent values.
Fοr example, the decimal number 125 can be represented in base 2 as 1111101, in base 8 as 175, and in base 16 as 7D.
Cοnverting a number frοm οne base tο anοther invοlves dividing the number by the base and repeatedly finding the remainder until the quοtient becοmes zerο. The remainders, read frοm bοttοm tο tοp, represent the digits οf the new number in the new base.
Tο cοnvert a number in base 3 tο base 10, we need tο multiply each digit οf the number by the cοrrespοnding pοwer οf 3, and then sum up the prοducts.
Starting frοm the rightmοst digit οf the number, the pοwers οf 3 increase by 1 fοr each digit tο the left. Sο, fοr the number 1406 (3 at the bοttοm), we have:
1 × 3⁰ + 0 × 3¹ + 4 × 3² + 1 × 3³ = 1 + 0 + 36 + 81 = 118
Therefοre, the base 10 representatiοn οf the number 1406 (3 at the bοttοm) is 118.
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The Bureau of Labor Statistics compiles and makes publicly available data from a range of different sectors of the economy. One value that is reported is a weighted average of the costs of certain goods, called the Consumer Price Index (CPI). The CPI is related to the price but is not a dollar amount. The rise in prices is used as a metric of inflation. To make the metric more reliable, a chained CPI was created. The regular CPI does not update the types of goods it averages often enough to reflect the market trends, like a switch from apples to oranges resulting from a rise in apple prices. The chained CPI is a measure of price that takes this into account, and there are several bills that are tied to the chained CPI index in order to determine the payout the bill allots each year. The monthly average chained CPI for urban apparel for all urban consumers for 10 consecutive months is provided below. The data are not seasonally adjusted. Construct a box and whisker plot using a TI-83, TI-83 Plus, or TI-84 graphing calculator to choose the correct plot below. All plots have the following window settings: Xmin=88, Xmax=100.5, Xscl=0.5, Ymin=−0.5, Ymax=3.5, Yscl=1, Xres=1.
Answer:
I can provide guidance on how to create a box and whisker plot on a TI-83, TI-83 Plus, or TI-84 graphing calculator using the given data.
To create a box and whisker plot:
Enter the data into a list on the calculator. For example, L1={90.1, 91.1, 91.5, 92.2, 92.5, 93.1, 94.0, 94.6, 96.1, 98.3}.
Press STAT, then go to Edit.
Select L1, then press STAT again and select CALC.
Choose 1-Var Stats and press Enter. This will generate a list of statistics for the data set.
Press 2nd, then Y= (STAT PLOT).
Select Plot1, then turn it on.
Choose Box Plot as the plot type.
Select L1 as the data list.
Set the X list to any unused list (e.g. Xlist: L2).
Make sure the frequency is set to 1.
Set the window settings as follows: Xmin=88, Xmax=100.5, Xscl=0.5, Ymin=−0.5, Ymax=3.5, Yscl=1, Xres=1.
Press GRAPH to view the box and whisker plot.
Note: If the plot does not display properly, try adjusting the Ymax and Ymin values until the plot is visible.
What is the difference?complete the stament -2-8=
Answer: -10
Step-by-step explanation: You're welcome <3
A trapezoid has a base of 5 millimeters,
another base of 7 millimeters, and a height
of 6 millimeters. Explain how the area of the
trapezoid will change if the height and both
bases are doubled.
The area of the trapezoid is multiplied by a factor of 4 when both bases and the height are doubled.
What is trapezoid ?Trapezoids can be defined as quadrilaterals that have two parallel sides and two non-parallel sides.
The area of a trapezoid is given by the formula:
A = (b1 + b2) * h / 2
Where
b1 and b2 are the lengths of the two basesh is the heightIf we double both bases and the height, we get:
b1' = 2 * b1 = 2 * 5 mm = 10 mm
b2' = 2 * b2 = 2 * 7 mm = 14 mm
h' = 2 * h = 2 * 6 mm = 12 mm
Now we can calculate the area of the new trapezoid:
A' = (b1' + b2') * h' / 2
A' = (10 mm + 14 mm) * 12 mm / 2
A' = 12 * 12 mm^2
A' = 144 mm^2
Therefore, the area of the trapezoid is multiplied by a factor of 4 when both bases and the height are doubled.
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Apnex, Inc. , is a biotechnology firm that is about to announce the results of its clinical trials of a potential new cancer drug. If the trials are successful, Apnex stock will be worth $ 68 per share. If the trials are unsuccessful, Apnex stock will be worth $ 18 per share. Suppose that the morning before the announcement is scheduled, Apnex shares are trading for $ 56 per share
The probability of the trials being successful is 0.625 or 62.5%. So, the expected value of Apnex stock after the announcement is $53.25 per share.
The odds of the trials being successful or failed, as well as the associated stock prices, must be taken into account in order to determine the predicted value of Apnex shares after the announcement.
we can state:
P(success) + P(failure) = 1
Let the market has already taken the probability into account and that the $56 stock price at the moment reflects the stock's anticipated value following the announcement. To put it another way, we can construct an equation based on the anticipated value formula:
Estimated Value = $68 for success and $18 for failure
Also, we are aware that the present stock price and the predicted value are equal:
Estimated Value = $56
When the second equation is substituted for the first equation, we obtain:
P(success) x $68 plus P(failure) x $18 equals $56.
For P(success), we obtain:
P(success) is equal to ($56 - $18) / ($68 - $18), or 0.625.
Thus, 0.625 or 62.5% of the trials will be successful.
We may determine the anticipated value of the shares following the announcement using this probability:
Estimated Value: 0.625 times $68 plus 0.375 times $18 equals $53.25
therefore, $53.25 per share is the anticipated value of Apnex shares following the announcement.
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Evaluate the expression shown below and write your answer as a
fraction in simplest form.
1/4 - 1/10
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The net of the pyramid is attached and the surface area of the triangular based prism is 54 ft²
The net of the pyramidThe shape is given as
A triangular based prism
This means that the net would have 2 triangles and 3 rectangles
See attachment for the net of the prism
How to determine the surface areaThe surface area of a triangular based prism is calculated as
Area = (Perimeter of triangle) * Length + 2 * Base area
Substitute the known values in the above equation, so, we have the following representation
Area = (3 + 2 1/2 + 2 1/2) * 6 + 2 * 0.5 * 2 * 3
Evaluate
Area = 54
Hence, the surface area is 54 ft²
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Find the surface area of the equilateral triangular pyramid.
A 180cm^2
B 228cm^2
C 268cm^2
D 456cm^2
The surface area of a triangular pyramid is the sum of areas of all faces of a triangular pyramid. Here, the surface area of a triangular pyramid with side 12 cm, base height 10 cm is equals to the 228 cm². So, the option (b) is correct choice.
Generally, a triangular pyramid has a triangular base and is bounded by three lateral triangular faces with one vertex. The units of measured surface area are square units like cm², m², ft² or cubit². The Formula for the surface area of a pyramid is calculated by adding up the area of all triangular faces of a pyramid. Mathematically,
Surface area = 1⁄2(a × b) + 3⁄2(b × s).
Where b --> the side of a pyramid
a --> the height of a base triangle, and
s --> the slant height of a pyramid. We have a triangular pyramid as present in above figure. Here height of base, a = 8 cm
slant height , s = 10 cm
side of a pyramid, b = 12 cm
So, Area of base triangle is, A1 = 1⁄2(a × b)
= (1/2)(8×12) = 48 cm²
Area of one triangular face = 1/2( b×s)
= 1/2( 12 × 10) = 60 cm²
Area of all triangular faces of a pyramid, A2 = 3× 60 = 180 cm²
The surface area of a pyramid = A1 + A2
= 48 + 180 = 228 cm²
Hence, required area is 228 cm².
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Complete question:
Find the surface area of the equilateral triangular pyramid. See the above
A 180cm^2
B 228cm^2
C 268cm^2
D 456cm^2
many people use scanners to read documents and store them into pdf file. to help determine which brand of scanner to buy, a student conducts an experiment in which 8 different documents were scanned by each of the two scanners that he is interested in. he records the number of errors made by each. can he infer that brand a (the more expensive scanner) is better than brand b? that is, is the mean number of errors for brand a less than brand b? use brand a as population 1 and brand b as population 2. assume a 5% level of significance. dat
The student can use a two-sample t-test to determine if there is a significant difference between the mean number of errors made by brand A and brand B. The two-sample t-test compares the means of two populations to determine if they are significantly different from each other.
The null hypothesis for this test is that the mean number of errors for brand A is equal to the mean number of errors for brand B. The alternative hypothesis is that the mean number of errors for brand A is less than the mean number of errors for brand B.
To conduct the two-sample t-test, the student will need to calculate the mean and standard deviation of the number of errors for each brand. Then, he will use the t-test formula to calculate the t-value and compare it to the critical value for a 5% level of significance.
If the t-value is less than the critical value, the student can reject the null hypothesis and conclude that the mean number of errors for brand A is significantly less than the mean number of errors for brand B. This would suggest that brand A is better than brand B.
However, if the t-value is greater than the critical value, the student cannot reject the null hypothesis and cannot conclude that there is a significant difference between the two brands.
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.Pam wants to make a snack mixture of three parts of dried fruit to every four parts of assorted nuts. How many pounds of dried fruit will she need to make 35 pounds of the mixture?
Answer:
15 pounds
Step-by-step explanation:
for every 3 parts of dry fruit , four parts of nuts are added.
we know the total composition of the mixture is 35 pounds.
The total Composition of the mixture will be 7 parts
3/7 is dry fruit
4/7 is assorted nut
we can multiply the dry fruit composition to total
= 3/7 * 35 = 3*5 = 15
Pam needs 15 pounds of dry fruit to make the mixture.
What is the volume of this cone?
Use ≈ 3.14 and round your answer to the nearest hundredth.
Height 9 m
Radius 4 m
cubic meters
A 20,000 gallon swimming pool contains 5000 gallons of water when a hose is placed in the pool and begins adding water at a rate of
1250 gallons per hour.
Use the Segment tool to plot a graph representing the volume of water in the pool over time from when the hose is placed in the pool
until the pool is full
Therefore , the solution of the given problem of unitary method comes out to be for each number of t, we can plot the points corresponding to the equation V(t) = 5000 + 1250t .
What is an unitary method?To accomplish the task, one may use this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, there might be an opportunity to interact with the item once more. Otherwise, every significant factor that affects how algorithmic evidence behaves will be gone.
Here,
=> V(t) = 5000 + 1250t
where V(t) represents the amount of water in the pool at moment t (in hours)
t equals time (in hours)
The pool initially has 5000 gallons of water in it, so we add that to the 1250 t of water introduced by the hose.
We can use the time period as the x-axis (horizontal axis) and the amount of water as the y-axis to graph this equation. (vertical axis).
For instance, we can select the water volume interval from 0 to 20,000 gallons and the time interval from 0 to 16 hours (when the pool is full).
Then, for each number of t, we can plot the points corresponding to the equation V(t) = 5000 + 1250t and connect them with a line in order to get the image.
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please answer i’m giving most of my points
Answer:
Aprove or deny a loan
Step-by-step explanation:
If the bank knows you can't pay them back they won't.
They choose this by checking your net worth.