If the force is 270 Newton and the area is 0.03 square meter, the pressure is equal to 9,000 N/m².
What is pressure?In Mathematics, pressure can be defined as a measure of the force exerted per unit area of an object or physical body. This ultimately implies that, it is usually measured in Newton per meter square.
How to calculate the pressure of an object?Mathematically, the pressure of a physical object can be calculated by using this formula:
P = F/A
Where:
P represents the pressure.F represents the force.A represents the area.By substituting the given parameters, we have:
Pressure, P = 270/0.03
Pressure, P = 9,000 N/m².
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Tell whether the ordered pair is a solution of the linear system.
(-2,-3).
y=3x+3.
y=-x-5
The given ordered pair is not a solution of the linear system.
What is linear equations?Linear equations are mathematical equations that describe the relationship between two or more variables in a straight line. They can be written in the form of:
y = mx + b
According to question:To check if the ordered pair (-2, -3) is a solution to the system of linear equations, we need to substitute x = -2 and y = -3 into both equations and see if they are satisfied.
For the first equation y = 3x + 3, we have:
-3 = 3(-2) + 3
-3 = -3
This is true, so (-2, -3) satisfies the first equation.
For the second equation y = -x - 5, we have:
-3 = -(-2) - 5
-3 = 3
This is false, so (-2, -3) does not satisfy the second equation.
Since (-2, -3) satisfies the first equation but not the second equation, it is not a solution to the system of linear equations. Therefore, the answer is no.
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You tell your parents that you will pay the 15% tip for dinner. The bill was $130.56. You have $20.
a. Do you have enough to pay the tip?
b. How much should the tip be?
Responses
Answers: Yes; $15.75 No; $22.30 Yes; $19.60 No; $20.15
Yes.$19.60. you have enough money to pay the 15% tip for the bill of $130.56, and the amount of the tip should be $19.60.
a. Do you have enough to pay the tip?
To determine if you have enough to pay the tip, you need to calculate 15% of the bill and compare it to the amount of money you have.
15% of $130.56 = 0.15 x $130.56 = $19.58
Since you have $20, you do have enough to pay the tip.
Therefore, the answer is "Yes".
b. How much should the tip be?
The tip should be 15% of the bill, which is $19.60.
Therefore, the answer is "$19.58".
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helpp subtracting polynomials
Answer: viedo yt
Step-by-step explanation:
if i was you go look at a yt viedo and it is easier becuase thats what helped me when i was in 6th grade we stared early so hope that helps
Answer:
choice C
Step-by-step explanation:
0 + 3x⁴ + 5x³ - 4x⁸ - 0
- (2x⁵ - 2x⁴ + 4x³ - 0 - 5)
= 2x⁵ +5x⁴ + x³ - 4x² + 5
Subtract column by column of like terms, put 0's where there is no like term, change signs inside the parentheses of the second expression because you are subtracting.
What type of dilation occurs with a scale factor of 1/4?
In response to the query, we can state that Hence, a reduction dilation is the kind of dilation that happens when the scale factor is 1/4.
what is dilation in transformation geometry ?Dilation is a transform that modifies an object's size. Dilation is a technique used to increase or decrease objects. An picture that is an exact duplicate of the original shape is produced as a result of this change. There is, however, a significant fluctuation in the shape. Dilation should result in a distortion of the initial form.
Dilations are transformations that alter an object's size without altering its shape. When an object dilates by a scale factor of 1/4, its size is decreased by a factor of 1/4, or 0.25.
This implies that each dimension of the object—its length, breadth, and height—will be multiplied by 1/4, or 0.25. For instance, if the original item was 8 units long, the dilated version would be 2 units long (8 x 1/4 = 2). The dilated item would have a width of 1.5 units if the initial object had a width of 6 units (6 x 1/4 = 1.5).
Hence, a reduction dilation is the kind of dilation that happens when the scale factor is 1/4.
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You have a 20-year annuity with a present value (that is, nest
egg) of $425,000. If the APR is 4.5%, what is the monthly yield?
Round your answer to the nearest cent. Monthly annuity yield =
$
The monthly yield of the 20-year annuity with a present value of $425,000 and an APR of 4.5% is $8,521.68.
What is monthly yield?Monthly yield refers to the return on an investment over a 12-month period. It is calculated by dividing the total return on an investment by the amount invested and multiplying it by 100 to get a percentage figure.
This is done by taking 1 plus the interest rate divided by the number of payments per year, raised to the number of years times the number of payments per year. In this case, the annuity factor is calculated as:
1 + 0.045/12)^(20*12) = 49.81961
Then, the monthly yield is determined by dividing the present value by the annuity factor. In this case, the monthly yield is calculated as:
$425,000 / 49.81961 = $8,521.68
Therefore, the monthly yield of the 20-year annuity with a present value of $425,000 and an APR of 4.5% is $8,521.68.
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Write an exponential function that passes through the points (1, 12) and (5, 972)
Answer:
Step-by-step explanation:
An exponential function can be written in the form y = ab^x, where a is the initial value and b is the base. To find the specific exponential function that passes through the points (1, 12) and (5, 972), we need to solve for a and b.
Using the point (1, 12), we get:
12 = ab^1
12 = ab
Using the point (5, 972), we get:
972 = ab^5
We can use the equation ab from the first point to solve for a in terms of b:
a = 12/b
Substituting this expression for a into the second equation, we get:
972 = (12/b)b^5
Simplifying this equation, we get:
972 = 12b^4
Dividing both sides by 12, we get:
81 = b^4
Taking the fourth root of both sides, we get:
b = 3
Substituting this value of b into the equation a = 12/b, we get:
a = 4
Therefore, the exponential function that passes through the points (1, 12) and (5, 972) is:
y = 4(3^x)
How do I do this like I really need help with this been on it for two hours not knowing what to do
The equation of the line in slope-intercept form is given as follows:
y = -5x - 8.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses tbe y-axis.The graph of the line crosses the y-axis at y = -8, hence the intercept b is given as follows:
b = -8.
When x increases by 1, y decays by 5, hence the slope m is given as follows:
m = -5/1
m = -5.
Hence the function is defined as follows:
y = -5x - 8.
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If one meter is approximately 3.28 feet, how many meters are in 20 feet?
Answer:
65.6
Step-by-step explanation:
1 meter = 3.28 feet
20 feet = 3.28 x 20
= 65.616798
= 65.6 (1 dp)
:)
Spice Parisienne is two-fifths ounce ground clovesone and one-fifth ounces ground nutmeg and one and one-fifth ounces ground gingerone and one-tenth ounces cinnamon. Latisha buys spices to make one batch of Spice Parisienne. Use estimation to decide whether she buys more or less than 4 ounces of spices. Explain your reasoning.
To estimate whether Latisha buys more or less than 4 ounces of spices, we can round the given amounts to the nearest whole number.
Two-fifths ounce is about 0.4 ounce.
One and one-fifth ounces is about 1.2 ounces.
One and one-tenth ounces is about 1.1 ounces.
Adding these rounded amounts gives:
0.4 + 1.2 + 1.1 = 2.7 ounces
Since 2.7 ounces is less than 4 ounces, we can conclude that Latisha buys less than 4 ounces of spices to make one batch of Spice Parisienne.
Algebraic expression
Constant
Variable
Algebraic operations
Term
Commutative property
Compare each of these.
Overall , an algebraic expression is a combination of constants, variables, and algebraic operations.
What is algebraic operations?Algebraic operations are mathematical operations (addition, subtraction, multiplication, and division) used to manipulate algebraic expressions.
Algebraic expression: An algebraic expression is a combination of variables, constants, and algebraic operations, such as addition, subtraction, multiplication, and division.
Constant: A constant is a fixed value that does not change throughout an algebraic expression. For example, in the expression 2x + 5, the constant is 5.
Variable: A variable is a symbol or letter that represents a value that can vary or change within an algebraic expression. For example, in the expression 2x + 5, the variable is x.
Algebraic operations: Algebraic operations are mathematical operations used to manipulate algebraic expressions.
Term: A term is a part of an algebraic expression that includes a constant or a variable, or a product of a constant and a variable. For example, in the expression 2x + 5, the terms are 2x and 5.
Commutative property: The commutative property of addition and multiplication states that the order of the terms in an expression can be changed without affecting the value of the expression. For example, a + b = b + a and ab = ba.
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On each trial of a digit span memory task, the participant is asked to read aloud a string of random digits. The participant must then repeat the digits in the correct order. If the participant is successful, the length of the next string is increased by one. For instance, if the participant repeats four digits successfully, she will hear five random digits on the next trial. The participant's score is the longest string of digits she can successfully repeat. A professor of cognitive psychology is interested in the number of digits successfully repeated on the digit span task among college students. She measures the number of digits successfully repeated for 36 randomly selected students. The professor knows that the distribution of scores is normal, but she does not know that the true average number of digits successfully repeated on the digit span task among college students is 7.06 digits with a standard deviation of 1.610 digits. The expected value of the mean of the 36 randomly selected students, M, is______. (Hint: Use the population mean and/or standard deviation just given to calculate the expected value of M.) The standard error of M is_____. (Hint: Use the population mean and/or standard deviation just given to calculate the standard error.)
The expected value of the mean of the 36 randomly selected students, M, is 7.06 digits and the standard error of the mean is 0.268 digits.
The expected value of the mean of the 36 randomly selected students can be calculated using the formula:
E(M) = μ
where μ is the population mean, which is given as 7.06 digits.
Therefore, expected value of mean of 36 randomly selected students is:
E(M) = 7.06 digits
The standard error of the mean (SE) can be calculated using the formula:
SE = σ / √(n)
where σ is the population standard deviation, which is given as 1.610 digits, and n is the sample size, which is 36 in this case.
Therefore, the standard error of the mean is:
SE = 1.610 / √(36) = 0.268 digits
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10 POINTS.CAN SOMEONE PLEASE HELP ME
Answer:
x = 60°
y = 60°
Step-by-step explanation:
The three angles of a triangle add up to 180°
In ΔWXY, 60 + 60 + x = 180°
=> 120 + x = 180
=> x = 180 - 120 = 60°
Since lines WZ and XY are parallel, x and y which are alternate interior angles must be equal
So y = x = 60°
Mary makes two blueberry pies
in two pie pans that are 6" in
diameter. What is the total area of
Mary's two pies?
Answer:
56.54862 in^2
Step-by-step explanation:
area = pi*radius^2
radius = 1/2 diameter
pi=3.14159.....
a=pi*3^2
a=3.14159*9
a=28.27431
two pies=56.54862
Roger starts with -$30 in his bank account. He withdraws $30. What is his account balance after he withdraws $30? Roger's account balance after he withdraws $30 is $???
.
Answer:-60
Step-by-step explanation:
You read that a statistical test at the a 0. 01 level has probability 0. 14 of making a type ii error when a specific alternative is true. What is the power of the test against this alternative?
The power of the test against the specific alternative is given by 1 minus the probability of making a Type II error. Therefore, the power is 0.86= 86%
In statistical hypothesis testing, the power of a test is the probability that it correctly rejects a null hypothesis when a specific alternative hypothesis is true. In this case, we are given that the test has a significance level of α = 0.01, which means that the test rejects the null hypothesis if the probability of obtaining the observed result, or one more extreme, under the null hypothesis is less than 0.01.
However, we also know that when a specific alternative hypothesis is true, the test has a probability of making a Type II error of 0.14. This means that there is a 14% chance that the test fails to reject the null hypothesis, even though the alternative hypothesis is true.
Therefore, the power of the test against this specific alternative hypothesis is given by 1 minus the probability of making a Type II error, which is:
Power = 1 - P(Type II error) = 1 - 0.14 = 0.86
So, the power of the test against the specific alternative hypothesis is 0.86 or 86%. This means that when the alternative hypothesis is true, the test correctly rejects the null hypothesis 86% of the time.
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Ts is tangent to the circle at u, find the value of x
The value of x for the given tangent on the circle is found to be :
x = 74.75.
Explain about the tangent chord theorem?According to the Tangent-Chord Theorem, the angle created by a chord and just a tangent line to a circle equals the inscribed angle on the chord's opposite side.
"The angle generated by a tangent to a circle or a chord is half of the angle measuring of the intercepted arc," is another way to state the Tangent-Chord theorem.
From the given data:
Line SUT is tangent on circle:
So,
Let the chord be UM.
∠TUM + 41° = 180° (linear pair)
∠TUM = 180° - 41°
∠TUM = 139°
Now, as per tangent chord theorem:
∠TUM = 1/2 * arc length (4x -21)
139° * 2 = 4x - 21
278 + 21 = 4x
299 = 4x
x = 299/4
x = 74.75
Thus, the value of x for the given tangent on the circle is found to be :
x = 74.75.
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Rowan is taking his siblings to get ice cream. they can't decide whether to get a cone or a cup because they want to get the most ice cream for their money. if w = 4 in, x =6 in, y = 6 in, z = 2 in, and the cone and cup are filled evenly to the top with no overlap, which container will hold the most ice cream? use 3.14 for π, and round your answer to the nearest tenth. a cone with a height of x and a radius of w, a cylinder with a diameter of y and a height of z the cup holds 56.52 in3 more ice cream than the cone. the cone holds 56.52 in3 more ice cream than the cup. the cup holds 43.96 in3 more ice cream than the cone. the cone holds 43.96 in3 more ice cream than the cup.
Therefοre , the sοlutiοn οf the given prοblem οf area cοmes οut tο be The cοne hοlds 43.96 in³mοre ice cream than the cup, sο that is the cοrrect respοnse.
What precisely is an area?Calculating hοw much space wοuld be needed tο fully cοver the οutside will reveal its οverall size. When determining the surface οf such a trapezοidal fοrm, the surrοundings are additiοnally taken intο accοunt. The surface area οf sοmething determines its οverall dimensiοns. The number οf edges here between cubοid's fοur trapezοidal extremities determines hοw much water it can hοld inside.
Here,
We must determine the vοlumes οf the cοne and the cup in οrder tο cοmpare hοw much ice cream each cοntainer can carry.
=> Cοne vοlume = (1/3)r²h.
=> Cup vοlume = (1/4)d²h
where r is the cοne's radius (w/2), h is the cοne's height (x), d is the cup's width (y), and z is the cup's height.
Inputting the numbers prοvided yields:
=> Cοne vοlume = (1/3)π(2²)(6) = 16π cubic inches
=> Cup vοlume = (1/4)π(6²)(2) = 9π cubic inches
As a result, the cοne has a larger capacity than the cup.
The cοne hοlds 43.96 in³mοre ice cream than the cup, sο that is the cοrrect respοnse.
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The cost of a fish dinner to the owner of the Golden Wharf restaurant is $6 55. The fish dinner is sold for $11. 55. Determine the percent markup
The markup percentage for the fish dinner at the Golden Wharf restaurant is approximately 76.34%.
How to calculate the markup percent?The markup percent is calculated by dividing the markup amount by the cost and then multiplying it by 100%. The markup is the difference between the selling price and the cost, so in this case:
markup = selling price - cost
markup = $11.55 - $6.55
markup = $5.00
So the markup is $5.00.
Now we can calculate the markup percent:
markup percent = (markup / cost) × 100%
markup percent = ($5.00 / $6.55) × 100%
markup percent = 76.34%
Therefore, the markup percentage for the fish dinner at the Golden Wharf restaurant is approximately 76.34%.
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what are the trig functions?
Answer:
sin
cos
tan
csc
sec
cot
Step-by-step explanation:
easy to remember that they are reciprocals of each other
Which of the following is a rational number?
Answer:
< because 1\2 is the same as .5 and .5 is less than 3
HELP ASAP is the relationship between the amount of dry dog food and the amount of wet dog food proportional the numbers are for dry god food (cups) (Y) there 4.5 6 9
for wet dog food (oz) (x) SHOW WORK THX
Yes, there is direct relatiοn in amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd.
If amοunt οf dry dοg fοοd is x and the amοunt οf wet dοg fοοd is y then the relatiοn is given as: x = 3y
Hοw tο find the prοpοrtiοnality?Tο determine whether the relatiοnship between the amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd is prοpοrtiοnal, we need tο check whether the ratiο οf the twο quantities remains cοnstant.
A) yes, there is direct relatiοn in amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd. as amοunt οf dry dοg fοοd increases there alsο increase in amοunt οf wet gοοd.
if amοunt οf dry dοg fοοd is x and the amοunt οf wet dοg fοοd is y then the relatiοn is given as:
x = 3y
fοr example lets take values frοm first rοw
4.5 = 3 × 1.5
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Complete question:
Which expression can be used to find the sum of the polynomials?
(9 − 3x²) + (−8x² + 4x + 5)
A [(-3x²)+(-8x²)] +4x+ [9+(-5)]
B [3x²+8x²]+4x+ [9+(-5)]
C [3x²+(-8x²)]+4x+ [9+5]
D [(-3x²)+(-8x²)] +4x+ [9+5]
The expression that can be used to find the sum of polynomials is:
D [(-3x²)+(-8x²)] +4x+ [9+5].
Explain about the sum of polynomials?Polynomials are sums containing terms that have the shape k⋅xⁿ, in which k is any number and n is a positive integer.
For particular, 3x+21x-51 is a polynomial. a description of polynomials. Polynomial addition is the process of adding like terms from two maybe more algebraic equations while maintaining the sign of each term. It closely resembles a typical addition procedure.The given polynomials:
(9 − 3x²) + (−8x² + 4x + 5)
Addition will be done in such a way that signs of each term will remain same.
Opening the brackets.
= 9 − 3x² −8x² + 4x + 5
Rewriting the expression as:
= − 3x² −8x² + 4x + 5 + 9
Arranging them in brackets again.
= [(-3x²)+(-8x²)] +4x+ [9+5]
Thus, the expression that can be used to find the sum of polynomials is:
D [(-3x²)+(-8x²)] +4x+ [9+5].
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the factors of 18.
Answer:
2*3*3=2*3^2
Step-by-step explanation:
18÷2=9
9÷3=3
3÷3=1
Answer:
See below.
Step-by-step explanation:
[tex]\textsf{We are asked to identify the factors of 18.}[/tex]
[tex]\large \fbox{\textsf{The factors of 18 are: 1, 2, 3, 6, 9, 18.}}[/tex]
[tex]\huge\fbox{What are Factors?}[/tex]
[tex]\textsf{Factors are 2 whole numbers that \bf{multiply} to become a \bf{given number.}}[/tex]
[tex]\textsf{One simple way to identify factors is to divide the given number by positive integers.}[/tex]
[tex]\large\boxed{\textsf{For example;}}[/tex]
[tex]\textsf{Find the factors of 12.}[/tex]
[tex]\mathtt{12 \div 1 = 12 \ (Factor)}\\\mathtt{12 \div 2 = 6 \ (Factor)}\\\mathtt{12 \div 3 = 4 \ (Factor)}\\\mathtt{12 \div 4 = 3 \ (Factor)}\\\mathtt{12 \div 5 = 2.4 \ (Not \ A \ Factor)}\\\mathtt{12 \div 6 = 2 \ (Factor)}[/tex]
[tex]\mathtt{12 \div 7 = 1.714... \ (Not \ A \ Factor)}\\\mathtt{12 \div 8 = 1.5 \ (Not \ A \ Factor)}\\\mathtt{12 \div 9 = 1.\bar{3} \ (Not \ A \ Factor)}\\\mathtt{12 \div 10 = 1.2 \ (Not \ A \ Factor)}\\\mathtt{12 \div 11 = 1.\bar{09} \ (Not \ a \ Factor)}\\\mathtt{12 \div 12 = 1 \ (Factor)}[/tex]
[tex]\large \fbox{\textsf{The factors of 12 are: 1, 2, 3, 4, 6, 12.}}[/tex]
[tex]\textsf{Let's do the same thing, but with 18.}[/tex]
[tex]\textsf{Find the factors of 18.}[/tex]
[tex]\mathtt{18 \div 1 = 18 \ (Factor)}\\\mathtt{18 \div 2 = 9 \ (Factor)}\\\mathtt{18 \div 3 = 6\ (Factor)}\\\mathtt{18 \div 4 = 4.5 \ (Not \ A \ Factor)}\\\mathtt{18 \div 5 = 3.6 \ (Not \ A \ Factor)}\\\mathtt{18 \div 6 = 3 \ (Factor)}[/tex]
[tex]\mathtt{18 \div 7 = 2.574... \ (Not \ A \ Factor)}\\\mathtt{18 \div 8 = 2.25 \ (Not \ A \ Factor)}\\\mathtt{18 \div 9 = 2 \ (Factor)}\\\mathtt{18 \div 10 = 1.8 \ (Not \ A \ Factor)}\\\mathtt{18 \div 11 = 1.\bar{63} \ (Not \ A \ Factor)}\\\mathtt{18 \div 12 = 1.5 \ (Not \ A \ Factor)}[/tex]
[tex]\mathtt{18 \div 13 = 1.384.. \ (Not \ A \ Factor)}\\\mathtt{18 \div 14 = 1.285.. \ (Not \ A \ Factor)}\\\mathtt{18 \div 15 = 1.2 \ (Not \ A \ Factor)}\\\mathtt{18 \div 16 = 1.125 \ (Not \ A \ Factor)}\\\mathtt{18 \div 17 = 1.0588.. \ (Not \ A \ Factor)}\\\mathtt{18 \div 18 = 1 \ (Factor)}[/tex]
[tex]\large \fbox{\textsf{The factors of 18 are: 1, 2, 3, 6, 9, 18.}}[/tex]
53 increased by 68% please help
Answer:
89.04
Step-by-step explanation:
To find 68% of 53, we can multiply 53 by 0.68:
68% of 53 = 0.68 x 53 = 36.04
So 53 increased by 68% is:
53 + 36.04 = 89.04
Therefore, 53 increased by 68% is 89.04.
In an office, each worker eats 2 biscuits per day. There are 20 workers in the office
every day of the week. Biscuits come in packets of 14 and cost £1.30 per packet.
a) How many biscuits are eaten in the office per week?
b) How much does the office spend on biscuits per week?
******
£...
Answer:
(a) 280
(b) £26
Step-by-step explanation:
(a) 20 workers eat 2 biscuits a day.
20 × 2 = 40
Since there are 7 days a week, multiply the 40 x 7 to find how many biscuits are eaten each week.
40 × 7 = 280
280 biscuits are eaten every week.
(b) Now, divide 280 (the number of biscuits eaten each week) by 14 (the number of biscuits in a packet) to find how many packets are eaten weekly.
280 ÷ 14 = 20
Now you have the number of packets eaten each week, so you can determine the price spent on biscuits. Multiply 20 packets by the price per packet, which is £1.30.
20 × 1.30 = 26
The office spends £26 on biscuits each week.
ACDF is a rectangle with an area of (2x² + 2x - 12)cm². B is a point on AC and E is a point on FD such that ABEF is a square with side lengths
of (x-2) cm each.
Calculate the length of ED.
The length of side ED is x + 8.
What is the length of side ED?
The length of side ED is calculated by applying the formula for area of a rectangle as shown below.
Let the length of ED = L
Then the total length of the rectangle ACDF = L + (x - 2)
The formula for area of a rectangle = Length x Base
where;
the length of the rectangle = L + x - 2the base of the rectangle = x - 2Area = L + (x - 2) · (x - 2)
(2x² + 2x - 12 ) = (x - 2 ) · (L + x - 2 )
2x² + 2x - 12 = xL + x² - 2x - 2L - 2x + 4
2x² + 2x - 12 = xL + x² - 4x - 2L + 4
x² + 6x - 16 = xL - 2L
x² + 6x - 16 = L (x - 2 )
L = (x² + 6x - 16) / ( x - 2)
divide using long division;
x + 8
------------
x - 2 √ x² + 6x - 16
- (x² - 2x)
----------
8x - 16
- (8x - 16)
---------
0
L = x + 8
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ED = 2x - 2 = 2[(13 + √65) / 7] - 2 = (26 + 2√65) / 7
Therefore, the length of ED is (26 + 2√65) / 7 cm.
54. Sally has an average score of exactly k points on 6 equally
weighted tests. How many points higher than k must Sally
score on the 7th equally weighted test to raise her average
score after the 7th test to k + 2.5 points?
PLEASE SHOW WORK
Answer:
Sally's score on the 7th test needs to be 17.5 points points more than the average of her first 6 tests.
Step-by-step explanation:
Let T be the sum of the scores of Sally's first 6 tests. Her average score would be:
Avg. Score (S) =T/6
Let S stand for Sally's average score.
We are told her average is k, so we can write: S = k
Let N stand for the score of her New (7th) test. Her total score would be:
T + N [This is the sum of all 7 of her tests]
Her average would become (T+N)/7
The goal is to raise her average score by 2.5 points to (k+2.5) points.
That means (T+N)/7 = k+2.5 [Her new average is 2.5 points higher]
(T + N)/7 = k + 2.5
T+N = 7k+17.5
Note that T = 6k [her total score for the first 6 tests is her average, k, times 6]
We'll use this definition of T in the equation:
T+N = 7k+17.5
(6k)+N = 7k+17.5 [Substitute 6k for T, since T=6k]
N = 7k+17.5-6k [Rearrange]
N = 1k+17.5
This is telling Sally, and us, that her new test, N, must score 17.5 points higher than her average score, k.
The answer is 17.5 points.
At the start of the day, a painter resteda 3 m ladder against a vertiçal wall So that the foot of the ladder was 50 cm away from the base of the wall. During the day, the ladder slipped down the wall, causing the foot of the ladder to move 70 cm further away from the base of the wall. How far down the wall, in centimetres, did the ladder slip? Give your anSwer to the nearest 1 cm.
The distance the ladder slipped down is 21cm.
How far down the wall did the ladder slip?The ladder, wall and the base of the wall form a right triangle. The ladder is the hypotenuse. The wall is the height and the distance of the foot of the ladder to the base of the wall is the base.
Pythagoras theorem would be used to determine the length of the wall.
The Pythagoras theorem: a² + b² = c²
where:
a = heightb = basec = hypotenuse100 cm = 1 meter
3 x 100 = 300 cm
a² + 50² = 300²
a² + 2500 = 90,000
a² = 90,000 - 2500
a² = 87,500
a = √87500
a = 296 cm
Height when the ladder slipped down:
(70 + 50)² + a² = 300²
120² + a² = 300²
14,400 + a² = 90,000
a² = 90,000 - 14,400
a² = 75,600
a = √75,600
a = 275
Distance the ladder slipped = 296- 275 = 21 cm
To learn more about Pythagoras theorem, please check: https://brainly.com/question/14580675
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A market researcher for a consumer electronics company wants to study the media viewing behavior of residents of a particular area. A random sample of 80 respondents is selected, and each respondent is instructed to keep a detailed record of time spent engaged viewing content across all screens in a particular week. The results are as follows: Content viewing time per week: X = 44 hours, S = 5.7 hours. 28 respondents have high definition (HD) on at least one television set. Complete parts (a) through (e) below. a. Construct a 90% confidence interval estimate for the mean content viewing time per week in this area. Isusa (Round to two decimal places as needed.) b. Construct a 90% confidence interval estimate for the population proportion of residents who have HD on at least one television set. Osas (Round to four decimal places as needed.) c. Suppose that the market researcher wants to take another survey in a different location. What sample size is required to be 90% confident of estimating the population mean content viewing time to within + 2 hours assuming that the population standard deviation is equal to 6 hours? (Type a whole number.) d. How many respondents need to be selected to be 90% confident of being within 10.05 of the population proportion who have HD on at least one television set if no previous estimate is available? (Type a whole number.) Enter your answer in each of the answer boxes. e. Based on (C) and (d), how many respondents should the market researcher select if a single survey is being conducted? (Type a whole number.) Enter your answer in each of the answer boxes.
a. Construct a 90% confidence interval estimate for the mean content viewing time per week in this area. Isusa
90% confidence interval estimate for the mean content viewing time per week: (41.75, 46.25)
b. Construct a 90% confidence interval estimate for the population proportion of residents who have HD on at least one television set. Osas
90% confidence interval estimate for the population proportion: (0.1867, 0.3833)
c. Suppose that the market researcher wants to take another survey in a different location. What sample size is required to be 90% confident of estimating the population mean content viewing time to within + 2 hours assuming that the population standard deviation is equal to 6 hours? (Type a whole number.)
Sample size required: 653
d. How many respondents need to be selected to be 90% confident of being within 10.05 of the population proportion who have HD on at least one television set if no previous estimate is available? (Type a whole number.) Enter your answer in each of the answer boxes.
Sample size required: 461
e. Based on (C) and (d), how many respondents should the market researcher select if a single survey is being conducted? (Type a whole number.) Enter your answer in each of the answer boxes.
Sample size required: 653
an angle that measures 125 is composed of 23 smaller angles two of the smaller angles measure of 25 and 40 Tom things you can use an equation 125+40-25 = s to find the measure of the unknown smaller angle s explain why Tom is incorrect, and tell how to find the measure of the third smaller angle s
Answer:
60
Step-by-step explanation:
The measure of the other angle is 60°.
What is an Angle ?
An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
As given in the question
An angle that measures 125° is composed of three smaller angles.
Two of the smaller angles measure 25° and 40 degrees
Tom thinks he can use the equation 25 degrees + (40 degrees - 25 degrees) = s to find the measure of the unknown smaller angle, s
Tom is incorrect because the sum of the smaller angles will be equal to the bigger angle and the equation he has written is wrong.
The right equation and method will be
25 +40+x = 125
x = 125-40-25
x = 60°
Therefore the measure of the other angle is 60°.