The completion of the statements about the number of students in Mr. Baker's class is as follows:
The number of students in his class must be a prime number.The quotient from the division of the students into equal-sized groups is not even because there must be a remainder.What is a prime number?A prime number is a number divisible by itself and 1 only.
When a prime number is divided by another number except by itself and 1, there is always a remainder in the quotient.
Some examples of the prime numbers in Mr. Baker's class include 19, 23, 29, 31, or 37 students.
Thus, these numbers of students cannot be divided by another number without a remainder because they are prime numbers.
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Question Completion:1. The number of students in his class must be a --- number.
2. The quotient from the division of the students into equal-sized groups is .... because there must be a .....
true or false 16/24 equals 30 / 45
True.
Given:
The equation is, 16/24 = 30/45.
The objective is to find true or false.
The equivalent fractions can be verified by, mutiplying the denominator and numerator of each fraction.
The fractions can be solved as,
[tex]\begin{gathered} \frac{16}{24}=\frac{30}{45} \\ 16\cdot45=24\cdot30 \\ 720=720 \end{gathered}[/tex]Since both sides are equal, the ratios are equivalent ratios.
Hence, the answer is true.
which description compass the domains of function a and function be correctly rest of the information in the picture below please answer with the answer choices
Given:
Function A: f(x) = -3x + 2
And the graph of the function B
We will compare the domains of the functions
Function A is a linear function, the domain of the linear function is all real numbers
Function B: as shown in the figure the graph starts at x = 0 and the function is graphed for all positive real numbers So, Domain is x ≥ 0
So, the answer will be the last option
The domain of function A is the set of real numbers
The domain of function B: x ≥ 0
At one time, it was reported that 27.9% of physicians are women. In a survey of physicians employed by a large health system, 45 of 120 randomly selected physicians were women. Is there sufficient evidence at the 0.05 level of significance to conclude that the proportion of women physicians in the system exceeds 27.9%?Solve this hypothesis testing problem by finishing the five steps below.
SOLUTION
STEP 1
The hull hypothesis can written as
[tex]H_0\colon p=0.279[/tex]The alternative hypothesis is written as
[tex]H_1\colon p>0.279[/tex]STEP 2
The value of p will be
[tex]\begin{gathered} \hat{p}=\frac{X}{n} \\ \hat{p}=\frac{45}{120}=0.375 \\ \text{where n=120, x=}45 \end{gathered}[/tex]STEP3
From the calculations, we have
[tex]\begin{gathered} Z_{\text{cal}}=2.34 \\ \text{Z}_{\text{los}}=0.05 \end{gathered}[/tex]We obtained the p-value has
[tex]\begin{gathered} p-\text{value}=0.0095 \\ \text{level of significance =0.05} \end{gathered}[/tex]STEP4
Since the p-value is less than the level of significance, we Reject the null hypothesis
STEP 5
Conclusion: There is no enought evidence to support the claim
The ship leaves at 18 40 to sail to the next port.
It sails 270 km at an average speed of 32.4 km/h
Find the time when the ship arrives.
Answer:
Step-by-step explanation:
Given:
t₁ = 18:40 or 18 h 40 min
S = 270 km
V = 32.4 km/h
____________
t₂ - ?
Ship movement time:
t = S / V = 270 / 32.4 ≈ 8.33 h = 8 h 20 min
t₂ = t₁ + t = 18 h 40 min + 8 h 20 min
40 min + 20 min = 60 min = 1 h
18 h +8 h = 26 h = 24 h + 2 h
2 h + 1 h = 3 h
t₂ = 3:00
The ship will arrive at the destination port at 3:00 the next day.
Answer:
32.4 - 27.0 = 5.4
18.40 + 54 =
7hrs:34mins
The ship arrived at
7:34pm
name the sets of numbers to which the number 62 belongs
62
real numbers (not imaginary or infinity)
rational numbers
Integers ( no fraction, included negative numbers)
Whole numbers (no fraction)
Natural numbers (counting and whole numbers)
Find the missing quantity with the information given. Round rates to the nearest whole percent and dollar amounts to the nearest cent% markdown = 40Reduced price = $144$ markdown = ?
The given information:
% mark up = 40
Reduced = $144
Markdown = ?
The formula for percentage markup is given as
[tex]\text{ \%markup }=\frac{markup}{actual\text{ price}}\times100[/tex]Let the actual price be x
Hence,
Reduced price = 60% of actual price
[tex]60\text{\% of x = 144}[/tex]Solving for x
[tex]\begin{gathered} \frac{60x}{100}=144 \\ x=\frac{144\times100}{60} \\ x=240 \end{gathered}[/tex]Therefore, actual price = $240
Inserting these values into the %markup formula gives
[tex]40=\frac{\text{markup}}{240}\times100[/tex]Solve for markup
[tex]\begin{gathered} 40=\frac{100\times\text{markup}}{240} \\ 40\times240=100\times\text{markup} \\ \text{markup}=\frac{40\times240}{100} \\ \text{markup}=96 \end{gathered}[/tex]Threefore, markup = $96
What is the current population of elk at the park?
Given the following function:
[tex]\text{ f\lparen x\rparen= 1200\lparen0.8\rparen}^{\text{x}}[/tex]1200 represents the initial/current population of elk in the national park.
Therefore, the answer is CHOICE A.
Radicals and Exponents Identify the choices that best completes the questions 3.
3.- Notice that:
[tex]\sqrt[]{12}=\sqrt[]{4\cdot3}=2\sqrt[]{3}\text{.}[/tex]Therefore, we can rewrite the given equation as follows:
[tex]2\sqrt[]{3}x-3\sqrt[]{3}x+5=4.[/tex]Adding like terms we get:
[tex]-\sqrt[]{3}x+5=4.[/tex]Subtracting 5 from the above equation we get:
[tex]\begin{gathered} -\sqrt[]{3}x+5-5=4-5, \\ -\sqrt[]{3}x=-1. \end{gathered}[/tex]Dividing the above equation by -√3 we get:
[tex]\begin{gathered} \frac{-\sqrt[]{3}x}{-\sqrt[]{3}}=\frac{-1}{-\sqrt[]{3}}, \\ x=\frac{1}{\sqrt[]{3}}\text{.} \end{gathered}[/tex]Finally, recall that:
[tex]\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{3}\text{.}[/tex]Therefore:
[tex]x=\frac{\sqrt[]{3}}{3}\text{.}[/tex]Answer: Option C.
From the diagram below, if side AB is 36 cm., side DE would be ______.
Given
AB = 36 cm
Find
Side DE
Explanation
here we use mid segment theorem ,
this theorem states that the mid segment connecting the mid points of two sides of a triangle is parallel to the third side of the triangle and the length of the midsegment is half the length of the third side.
so , DE = 1/2 AC
DE = 36/2 = 18 cm
final Answer
therefore , the correct option is c
1. Write the equation of a line perpendicular to thex 5and that passes through thepoint (6,-4).line y
The line we want has a slope that is the negative reciprocal of the slope of the line
y = -(1/2)x - 5
The slope of this line is -1/2. So, the slope of its perpendicular lines is 2. Therefore, their equations have the form:
y = 2x + b
Now, to find b, we use the values of the coordinates of the point (6, -4) in that equation:
-4 = 2*6 + b
-4 = 12 + b
b = -4 - 12 = -16
Therefore, the equation is y = 2x - 16.
THIS IS URGENT
A line includes the points (2,10) and (9,5). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answer:
Step-by-step explanation:
y = 13x -12
What is the y-intercept of the line x+2y=-14? (0,7) (-7,0) (0,-7) (2,14)
1. Is this figure a polygon?2. Is this polygon concave or convex?3. Is this polygon regular, equiangular, Equilateral, or none of these?4. What is the name of this polygon?
A polygon is a closed shape with straigh sides, then
2. Is the figure a polygon? YES.
Since the figure is a polygon
1a. Is this polygon concave or convex? It is concave. A concave polygon will always have at least one reflex interior angle, tha is, it has on interior angle greater than 180 degrees.
1b. Is this polyogn regular, equiangular, equilateral or none of these? The marks on the picture mean that all the sides have the same length. This is the definition of equilateral. Then the answer is equilateral.
1c. What is the name of this polygon? We can see it has 4 equal sides and is concave, then his name is Concave Equilateral Quadrilateral.
The lengths of adult males' hands are normally distributed with mean 189 mm and standard deviation is 7.4 mm. Suppose that 15 individuals are randomly chosen. Round all answers to 4 where possible.
a. What is the distribution of ¯x? x¯ ~ N( , )
b. For the group of 15, find the probability that the average hand length is less than 191.
c. Find the first quartile for the average adult male hand length for this sample size.
d. For part b), is the assumption that the distribution is normal necessary? No Yes
Considering the normal distribution and the central limit theorem, it is found that:
a) The distribution is: x¯ ~ N(189, 1.91).
b) The probability that the average hand length is less than 191 is of 0.8531 = 85.31%.
c) The first quartile is of 187.7 mm.
d) The assumption is necessary, as the sample size is less than 30.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]. The mean is the same as the population mean.For sample size less than 30, such as in this problem, the assumption of normality is needed to apply the Central Limit Theorem.The parameters in this problem are given as follows:
[tex]\mu = 189, \sigma = 7.4, n = 15, s = \frac{7.4}{\sqrt{15}} = 1.91[/tex]
Hence the sampling distribution of sample means is classified as follows:
x¯ ~ N(189, 1.91).
The probability that the average hand length is less than 191 is the p-value of Z when X = 191, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (191 - 189)/1.91
Z = 1.05
Z = 1.05 has a p-value of 0.8531, which is the probability.
The first quartile of the distribution is X when Z has a p-value of 0.25, so X when Z = -0.675, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
-0.675 = (X - 189)/1.91
X - 189 = -0.675 x 1.91
X = 187.7 mm.
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In July, Lee Realty sold 10 homes at the following prices: $140,000; $166,000; $80,000; $98,000; $185,000; $150,000; $108,000; $114,000; $142,000; and $250,000. Calculate the mean and median.
The mean is 143000 and Median is 141000 for data $140,000; $166,000; $80,000; $98,000; $185,000; $150,000; $108,000; $114,000; $142,000; and $250,000.
What is Statistics?A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data
The mean is give by sum of n numbers to the total number of observations
Mean=Sum of observations/ Number of observations
Given,
10 homes at the following prices: $140,000; $166,000; $80,000; $98,000; $185,000; $150,000; $108,000; $114,000; $142,000; and $250,000.
Sum of observations=$140,000+$166,000+$80,000+$98,000+ $185,000+$150,000+ $108,000+$114,000+$142,000+ $250,000=1433000
n=10
Mean=1433000/10=143000
So mean is 143000
Now let us find the median, Median is the middle most number.
First we have to arrange the observation in ascending order.
$80,000, $98,000, $108,000, $114,000, $140,000, $142,000, $150,000, $166,000, $185,000, $250,000
Now Median= ($140,000+$142,000)/2
=282000/2=141000
Hence Mean is 143000 and Median is 141000.
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how to get standar form from point 1,4 and a slope of 5
In exercises 1 and 2 , identify the bisector of ST then find ST
Given: The line segment ST as shown in the image
To Determine: The bisector of ST and the value of ST
Solution
It can be observed from the first image, the bisector of ST is line MW
[tex]\begin{gathered} ST=SM+MT \\ SM=MT(given) \\ MT=19(given) \\ Therefore \\ ST=19+19 \\ ST=38 \end{gathered}[/tex]For the second image, the bisector of ST is line LM
[tex]\begin{gathered} ST=SM+MT \\ SM=3x-6 \\ MT=x+8 \\ SM=MT(given) \\ Therefore \\ 3x-6=x+8 \\ 3x-x=8+6 \\ 2x=14 \\ x=\frac{14}{2} \\ x=7 \end{gathered}[/tex][tex]\begin{gathered} SM=3(7)-6=21-6=15 \\ MT=7+8=15 \\ ST=SM+MT \\ ST=15+15 \\ ST=30 \end{gathered}[/tex]For first exercise, the bisector is MW, ST = 38
For the second exercise, the bisector is LM, ST = 30r
Write the following phrase as a variable expression. Use x to represent “a number” The sum of a number and fourteen
we can write "the sum of a number and fourteen", given that x represents any number, like this:
[tex]x+14[/tex]I don't get any of this help me please
Using scientific notation, we have that:
a) As an ordinary number, the number is written as 0.51.
b) The value of the product is of 1445.
What is scientific notation?An ordinary number written in scientific notation is given as follows:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1.
For item a, to add one to the exponent, making it zero, we need to divide the base by 10, hence the ordinary number is given as follows:
5.1 x 10^(-1) = 5.1/10 = 0.51.
For item b, to multiply two numbers, we multiply the bases and add the exponents, hence:
(1.7 x 10^4) x (8.5 x 10^-2) = 1.7 x 8.5 x 10^(4 - 2) = 14.45 x 10².
To subtract two from the exponent, making it zero, we need to multiply the base by 2, hence the base number is given as follows:
14.45 x 100 = 1445.
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A committee of six people is chosen from five senators and eleven representatives. How many committees are possiblethere are to be three senators and three representatives on the Committee
SOLUTION
This means we are to select 3 persons from 5 senators and 3 persons from 11 representatives. This can be done by
[tex]^5C_3\times^{11}C_3\text{ ways }[/tex]So we have
[tex]\begin{gathered} ^5C_3\times^{11}C_3\text{ ways } \\ 10\times165 \\ =1650\text{ ways } \end{gathered}[/tex]Hence the answer is 1650 ways
A man realizes he lost the detailed receipt from the store and only has the credit card receipt with theafter-tax total. If the after-tax total was $357.06, and the tax rate in the area is 8.2%, what was the pre-tax subtotal?
Answer: the pre-tax subtotal is $330
Explanation:
Let x represent the pre tax total
If the tax rate in the area is 8.2%, it means that the amount of tax paid is
8.2/100 * x = 0.082x
pretax total + tax = after tax subtotal
Given that after tax subtotal is $357.06, then
x + 0.082x = 357.06
1.082x = 357.06
x = 357.06/1.082
x = 330
the pre-tax subtotal is $330
gus bought 2/3 pound of turkey and 1/4 pound of ham.The tukey cost 9 dollars per pound, and the ham cost 7 dollars per pound.In all,how much did Gus spend?
From the information given,
gus bought 2/3 pound of turkey. If tukey costs 9 dollars per pound, it means that the cost of 2/3 pound of turkey is
2/3 x 9 = 6
gus bought 1/4 pound of ham. If ham costs 7 dollars per pound, it means that the cost of 1/4 pound of ham is
1/4 x 7 = 7/4 = 1.75
Total amount spent = amount spent on turkey + amount spent on ham
Total amount = 6 + 1.75
Total amount = $7.75
What is the vertex of the parabola with thefunction rule f(x) = 5(x − 4)² + 9?
The equation f(x) = a(x - h)^2 + k gives the vertex of the parabola--it is (h, k).
In this question, h = 4 and k = 9. So the vertex is at (4, 9).
2. Assume that each situation can be expressed as a linear cost function and find the appropriate cost function. (a) Fixed cost, $100; 50 items cost $1600 to produce. (b) Fixed cost, $400; 10 items cost $650 to produce. (c) Fixed cost, $1000; 40 items cost $2000 to produce. (d) Fixed cost, $8500; 75 items cost $11,875 to produce. (e) Marginal cost, $50; 80 items cost $4500 to produce. (f)Marginal cost, $120; 100 items cost $15,800 to produce. (g) Marginal cost, $90; 150 items cost $16,000 to produce. (h) Marginal cost, $120; 700 items cost $96,500 to produce.
Given:
Cost function is defined as,
[tex]\begin{gathered} C(x)=mx+b \\ m=\text{marginal cost} \\ b=\text{fixed cost} \end{gathered}[/tex]a) Fixed cost = $100, 50 items cost $1600.
The cost function is given as,
[tex]\begin{gathered} C=\text{Fixed cost+}x(\text{ production cost)} \\ x\text{ is number of items produced} \\ \text{Given that, }50\text{ items costs \$1600} \\ 1600=100\text{+50}(\text{ production cost)} \\ \text{production cost=}\frac{1600-100}{50} \\ \text{production cost}=30 \end{gathered}[/tex]So, the cost function is,
[tex]C=30x+100[/tex]b) Fixed cost = $400, 10 items cost $650.
[tex]\begin{gathered} 650=400+10p \\ 650-400=10p \\ p=25 \\ \text{ Cost function is,} \\ C=25x+400 \end{gathered}[/tex]c) Fixed cost= $1000, 40 items cost $2000 .
[tex]\begin{gathered} 2000=1000+40p \\ p=25 \\ C=25x+1000 \end{gathered}[/tex]d) Fixed cost = $8500, 75 items cost $11,875.
[tex]\begin{gathered} 11875=8500+75p \\ 11875-8500=75p \\ p=45 \\ C=45x+8500 \end{gathered}[/tex]e) Marginal cost= $50, 80 items cost $4500.
In this case we know the value of m = 50 .
Use the slope point form,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(80,4500) \\ y-4500=50(x-80) \\ y=50x-4000+4500 \\ y=50x+500 \\ C=50x+500 \end{gathered}[/tex]f) Marginal cost=$120, 100 items cost $15,800.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(100,15800) \\ y-15800=120(x-100) \\ y=120x-12000+15800 \\ y=120x+3800 \\ C=120x+3800 \end{gathered}[/tex]g) Marginal cost= $90,150 items cost $16,000.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(150,16000) \\ y-16000=90(x-150) \\ y=90x-13500+16000 \\ y=90x+2500 \\ C=90x+2500 \end{gathered}[/tex]h) Marginal cost = $120, 700 items cost $96,500
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(700,96500) \\ y-96500=120(x-700) \\ y=120x-84000+96500 \\ y=120x+12500 \\ C=120x+12500 \end{gathered}[/tex]The seventh term of a geometric sequence is 1/4 The common ratio 1/2 is What is the first term of the sequence?
Answer:
16
Explanation:
The equation for the term number n on a geometric sequence can be calculated as:
[tex]a_n=a_{}\cdot r^{n-1}[/tex]Where r is the common ratio and a is the first term of the sequence.
So, if the seventh term of the sequence is 1/4 we can replace n by 7, r by 1/2, and aₙ by 1/4 to get:
[tex]\frac{1}{4}=a\cdot(\frac{1}{2})^{7-1}[/tex]Then, solving for a, we get:
[tex]\begin{gathered} \frac{1}{4}=a(\frac{1}{2})^6 \\ \frac{1}{4}=a(\frac{1}{64}) \\ \frac{1}{4}\cdot64=a\cdot\frac{1}{64}\cdot64 \\ 16=a \end{gathered}[/tex]So, the first term of the sequence is 16.
Rewrite 20 - 4x³ using a common factor.
O 4x(5-x²)
O4(5 - 4x³)
02x(10-2x²)
02(10-2x³)
Answer:
[tex]20 - 4 {x}^{3} = 4(5 - {x}^{3} )[/tex]
Rewrite 4x + 16 using a common factor.
Answer 4(x + 4)
Solve for x using the quadratic formula.3x^2 +10x+8=3
The quadartic equation is 3x^2+10x+8=3.
Simplify the quadratic equation to obtain the equation in standard form ax^2+bx+c=0.
[tex]\begin{gathered} 3x^2+10x+8=3 \\ 3x^2+10x+5=0 \end{gathered}[/tex]The coefficent of x^2 is a=3, coefficient of x is b=10 and constant term is c=5.
The quadartic formula for the values of x is,
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Substitute the values in the formula to obtain the value of x.
[tex]\begin{gathered} x=\frac{-10\pm\sqrt[]{(10)^2-4\cdot3\cdot5}}{2\cdot3} \\ =\frac{-10\pm\sqrt[]{100-60}}{6} \\ =\frac{-10\pm\sqrt[]{40}}{6} \\ =\frac{-10\pm2\sqrt[]{10}}{6} \\ =\frac{-5\pm\sqrt[]{10}}{3} \end{gathered}[/tex]The value of x is,
[tex]\frac{-5\pm\sqrt[]{10}}{3}[/tex]Jason is making bookmarks to sell to raise money for the local youth center. He has 29 yards of ribbon, and he plans to make 200 bookmarks.Approximately how long is each bookmark, in centimeters?
The Solution:
The correct answer is 13.26 centimeters.
Explanation:
Given that Jason has 29 yards of ribbon, and he plans to make 200 bookmarks.
We are asked to find the approximate length (in centimeters) of each bookmark.
Step 1:
Convert 29 yards to centimeters.
[tex]\begin{gathered} \text{ Recall:} \\ \text{ 1 yard = 91.44 centimeters} \end{gathered}[/tex]So,
[tex]29\text{ yards = 29}\times91.44=2651.76\text{ centimeters}[/tex]Step 2:
To get the length of each bookmark, we shall divide 2651.76 by 200.
[tex]\text{ Length each bookmark = }\frac{2651.76}{200}=13.2588\approx13.26\text{ centimeters}[/tex]Therefore, the correct answer is 13.26 centimeters.
find the point that is symmetric to the point (-7,6) with respect to the x axis, y axis and origin
Answer:
[tex]\begin{gathered} a)(-7,-6)\text{ } \\ b)\text{ (7,6)} \\ c)\text{ (7,-6)} \end{gathered}[/tex]Explanation:
a) We want to get the point symmetric to the given point with respect to the x-axis
To get this, we have to multiply the y-value by -1
Mathematically, we have the symmetric point as (-7,-6)
b) To get the point that is symmetric to the given point with respect to the y-axis, we have to multiply the x-value by -1
Mathematically, we have that as (7,6)
c) To get the point symmetric with respect to the origin, we multiply both of the coordinate values by -1
Mathematically, we have that as:
(7,-6)
Find the percent change to the nearest percent for the function following
f(x) = 3(1 -.2)^-x
The percentage change of the function given in the task content as required is; 20%.
Percent change in exponential functions.It follows from the task content that the percentage change of the function is to be determined.
The percentage change in exponential functions is represented by the change factor, an expression on which the exponent is applied.
On this note, since the function given is an exponential function in which case, the change factor is; (1 - .2).
It consequently follows that the change implies a 20% decrease. This follows from the fact that 20% is equivalent to; 0.2.
Ultimately, the percentage change of the function is; 20%.
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