Answer:
Total length of iron needed to make the square frame and two diagonals = 43.44 in (Approx)
Step-by-step explanation:
Given:
Length of diagonal = 9 in
Find:
Total length of iron needed to make the square frame and two diagonals.
Computation:
Area of square = 1/2(diagonal)²
Area of square = 1/2(9)²
Area of square = 40.5 in²
Area of square = Side × Side
40.5 in² = Side × Side
Side = 6.36 (approx)
Total length of iron needed to make the square frame and two diagonals = Permeter of square + (2 × diagonal)
⇒ (4 × 6.36) + (2 × 9)
⇒ (25.44) + (18)
⇒ 43.44 in
Total length of iron needed to make the square frame and two diagonals = 43.44 in (Approx)
The Sears Tower, at 1,451 feet, is one of the tallest structures in the United States. A penny is thrown from the top of the tower. The height, h, of the penny is recorded after each second, t, in the table. Write an equation for the curve of best fit, then find the approximate height of the penny after 7 seconds.
Answer:
The equation for the height of the penny in function of time is:
[tex]h(t)=1451-16t^2[/tex]
After 7 seconds, the penny will be at a height of 667 feet.
Step-by-step explanation:
The penny will have a free fall.
The initial velocity is zero, and the initial height is h(0)=1,451.
The acceleration will be the gravity, that has a value g=32 ft/s^2.
Then, we can model this starting by the speed:
[tex]dv/dt=-g\\\\v(t)=v_0-gt=-gt[/tex]
Then, the height becomes:
[tex]dh/dt=v(t)=-gt\\\\h(t)=h_0-\dfrac{gt^2}{2}=1451-\dfrac{32}{2}t^2\\\\\\h(t)=1451-16t^2[/tex]
The approximate height of the penny after 7 seconds can be calculated as:
[tex]h(7)=1451-16(7^2)=1451-16*49=1451-784=667[/tex]
After 7 seconds, the penny will be at a height of 667 feet.
Of all rectangles with a perimeter of 29, which one has the maximum area? (Give the dimensions.) Let A be the area of the rectangle. What is the objective function in terms of the width of the rectangle, w? Aequals 14.5 w minus w squared (Type an expression.) The interval of interest of the objective function is nothing. (Type your answer in interval notation. Use integers or simplified fractions for any numbers in the expression.) The rectangle that has the maximum area has length nothing and width nothing. (Simplify your answer.)
Answer:
For maximum area: Its a square of dimensions 7.25 * 7.25.
Step-by-step explanation:
We can use calculus to solve this:
Let the length of the rectangle be L and the width be W then we have
2L + 2W = 29
L + W = 14.5
W = 14.5 - L
Area = WL
A = L(14.5 - L)
A = 14.5L - L^2
We need this to be a maximum.
Finding the derivative:
dA/dW = 14.5 - 2L = 0 for a maximum
2L = 14.5
L = 7.25
Also W = 14.5 - L
= 14.5 - 7.25 = 7.25.
So the dimensions for maximum area are 7.25 * 7.25.
The figure is a SQUARE.
The perimeter of a rectangle, is the sum of its side lengths.
The rectangle that has the maximum area when the length is 7.25 and the width is 7.25
The perimeter is given as:
[tex]\mathbf{P = 29}[/tex]
Let the dimensions be l and w.
So, we have:
[tex]\mathbf{2( l + w) = 29}[/tex]
Divide both sides by 2
[tex]\mathbf{l + w = 14.5}[/tex]
Make l the subject
[tex]\mathbf{l = 14.5 - w}[/tex]
The area of a rectangle is:
[tex]\mathbf{A = lw}[/tex]
Substitute [tex]\mathbf{l = 14.5 - w}[/tex]
[tex]\mathbf{A = (14.5 - w)w}[/tex]
Open brackets
[tex]\mathbf{A = 14.5w - w^2}[/tex]
Differentiate
[tex]\mathbf{A' = 14.5 - 2w}[/tex]
Set to 0
[tex]\mathbf{14.5 - 2w = 0}[/tex]
Collect like terms
[tex]\mathbf{2w = 14.5}[/tex]
Divide both sides by 2
[tex]\mathbf{w = 7.25}[/tex]
Recall that: [tex]\mathbf{l = 14.5 - w}[/tex]
So, we have:
[tex]\mathbf{l = 14.5 - 7.25 = 7.25}[/tex]
Hence, the rectangle that has the maximum area when the length is 7.25 and the width is 7.25
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In a recent poll, 30 percent of adults said they wanted to "cut down or be free of gluten," according to The NDP Group, the market-research company that conducted the poll. A researcher wonders if a smaller proportion of students at her university would respond in the same fashion. Suppose the researcher conducts a survey of a random sample of 25 students at her university and five of them say they want to at least reduce gluten. A statistician carries out a significance test of the null hypothesis that the proportion wanting to reduce gluten at the university is the same as for all adults versus the alternative hypothesis that a smaller proportion p of students would say they want to reduce or be free of gluten. What is the value of the standardized test statistic for this significance test? A) – 0.100 B) – 1.250 C) 0.200 D) – 1.091
Answer:
The value of the standardized test statistic for this significance test is -1.25.
Step-by-step explanation:
We are given that in a recent poll, 30 percent of adults said they wanted to "cut down or be free of gluten".
The researcher conducts a survey of a random sample of 25 students at her university and five of them say they want to at least reduce gluten.
Let p = population proportion of students wanting to reduce gluten at the university.
So, Null Hypothesis, [tex]H_0[/tex] : p = 30% {means that the proportion wanting to reduce gluten at the university is the same as for all adults}
Alternate Hypothesis, [tex]H_A[/tex] : p < 30% {means that a smaller proportion of students would say they want to reduce or be free of gluten}
The test statistics that would be used here One-sample z test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt\frac{\hat p(1-\hat p)}{n} {} }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of students who would say they want to reduce or be free of gluten = [tex]\frac{5}{25}[/tex] = 0.20
n = sample of students taken = 25
So, the test statistics = [tex]\frac{0.20-0.30}{\sqrt\frac{0.20(1-0.20)}{25} {} }[/tex]
= -1.25
The value of standardized z test statistic is -1.25.
Using the z-distribution, it is found that the value of the standardized test statistic for this significance test is:
D) –1.091
At the null hypothesis, we test if the proportion is of 0.3, that is:
[tex]H_0: p = 0.3[/tex]
At the alternative hypothesis, we test if the proportion is of less than 0.3, that is:
[tex]H_1: p < 0.3[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the parameters are:
[tex]p = 0.3, n = 25, \overline{p} = \frac{5}{25} = 0.2[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.2 - 0.3}{\sqrt{\frac{0.3(0.7)}{25}}}[/tex]
[tex]z = -1.091[/tex]
A similar problem is given at https://brainly.com/question/24166849
An important part of the customer-service responsibilities of a telephone company relates to the speed with which trouble in residential service can be repaired. Suppose that past data indicates that the probability is 0.9 that troubles in residential can be repaired in the same day. For the first five troubles reported on a given day. What is the probability that all troubles will be repaired in the same day
Answer:
59.05% probability that all troubles will be repaired in the same day
Step-by-step explanation:
For each trouble, there are only two possible outcomes. Either it can be repaired on the same day, or it cannot. The probability of a trouble being repaired on the same day is independent of other troubles. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Suppose that past data indicates that the probability is 0.9 that troubles in residential can be repaired in the same day
This means that [tex]p = 0.9[/tex]
For the first five troubles reported on a given day. What is the probability that all troubles will be repaired in the same day
This is P(X = 5) when n = 5. Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.9)^{5}.(0.1)^{0} = 0.5905[/tex]
59.05% probability that all troubles will be repaired in the same day
Can someone help me please
given the function defined below, what is the value of the 4th term?
f (1) = -4
f (n) = -3f (n-1) +5
f (4) =
Answer:
The 4 t h term is f(4) = 143
Step-by-step explanation:
Explanation:-
Given function f(1) = -4
Given 'nth' term is f(n) = -3f(n-1) +5
Put n =2 f(2) = -3 f(2-1) +5
= -3 f(1) +5
= -3 (-4) +5
= 12 +5
f(2) = 17
put n= 3
f(n) = -3f(n-1) +5
f(3) = -3 f(3-1) +5
= -3f(2) +5
= -3(17) +5
= -51+5
f(3) = -46
Put n=4
f(n) = -3f(n-1) +5
f(4) = -3f(4-1) +5
f(4) = -3f(3)+5
f(4) = -3(-46)+5
f(4) = 138 +5
f(4) = 143
Final answer:-
The 4 t h term is f(4) = 143
Cody paid $24.00 to join an online music service. If she purchases 15 songs each month at a cost of $1.25 per song, what will be the total amount she has spent after 6 months?
15 songs x 1.25 per song = $18.75 per month for songs.
18.75 per month x 6 months = $112.50
112.50 + 24.00 = $136.50 total
The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 52 and a standard deviation of 5. Using the empirical rule, what is the approximate percentage of lightbulb replacement requests numbering between 47 and 52
Answer:
34% of lightbulb replacement requests numbering between 47 and 52
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 52
Standard deviation = 5
Between 47 and 52:
52 is the mean and 47 is one standard deviation below the mean.
By the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean.
Since the normal distribution is symmetric, of those, 34% are within 1 standard deviation below the mean and the mean(47 and 52) and 34% are within the mean and one standard deviation above the mean(52 and 57).
So
34% of lightbulb replacement requests numbering between 47 and 52
A wedge of cheese in the shape of a triangular prism is shown below.
Find the surface area of the cheese.
_______Square feet
Answer:
[tex]144 $ Square feet[/tex]
Step-by-step explanation:
The given triangular prism comprises of two equal right triangles and three rectangles.
The Surface Area of the Prism
=Area of Two Triangles + Area of Three Rectangles
[tex]=2(0.5X6X8)+(6X4)+(10X4)+(8X4)\\=48+24+40+32\\=144 $ Square feet[/tex]
Answer: 144
Step-by-step explanation:32+24+4-+48=144
You take out a bagel and place it in the toaster for 5 minutes the toaster uses 1050 watts/hour
Parallel lines s and t are cut by a transversal, r.
Parallel lines s and t are cut by transversal r. Clockwise from top left, the angles formed with r and s are 1, 2, 3, 4; the angles formed with r and t are 5, 6, 7, 8.
If the measure of angle 1 is 68°, what is the measure of angle 5?
22°
68°
112°
158°
Answer:
68°
Step-by-step explanation:
Angles 1 and 5 are corresponding angles on parallel lines, hence they are equal
Answer:
B.
Step-by-step explanation:
1. A car priced at $25,329 is financed with a simple interest rate of 4.25% for 5 years with no down payment. Payments of $511.86 are made each month. Another car priced at $22,464 is financed with a simple interest rate of 3.78% for 5 years with a down payment of $2,500. Payments of $395.62 are made each month. a. For each loan, generate a table, graph, and equation that can be used to represent the balance after the down payment, if applicable, and the first 12 months of payments. The tables should represent the number of months in terms of x and the balance of the loan after each month’s payment in terms of y. b. Determine the rate of change, or slope, of each line and state the y-intercepts. c. Using your generated graph for the first situation, describe how the unit rate of the amount of money paid monthly is related to the slope of the line. d. Determine if each relationship represented in the table, graph, and equation represents a proportional or non- proportional situation. e. Use a set of ordered pairs, table, mapping, or graph to determine if each relationship represents a function.
Answer:
Step-by-step explanation:
Car 1
Price of the car $25,329
Add Interest ($25,329 * 4.25% / 12 * 12 * 5) = $5382.41
Total amount to be paid $30711.41
X Y
0 30711.41
1 30199.55
2 29689.69
3 29175.83
4 28663.97
5 28152.11
6 27640.25
7 27128.39
8 26616.53
9 26104.67
10 25592.81
11 25080.95
12 24569.09
Equation
Y = 30711.41 - 511.86 * x
Car 2
Price of the car $22,464
Less down payment - $2500
Amount to be financed $19964
Add interest (19964 * 3.78% / 12 * 12 * 5) $3773.20
Total amount to be paid $23737.20
X Y
0 23737.20
1 23341.58
2 22945.96
3 22550.34
4 22154.72
5 21759.10
6 21363.48
7 20967.86
8 20572.24
9 20176.62
10 19781.00
11 19385.38
12 18989.76
Equation
Y = 23737.20 - 395.62 * x
b) Determine the rate of change, or slope, of each line and state the y-intercepts
Car 1 Car 2
Slope of each line 511.86 395.62
Y intercept 30711.41 23737.20
c) Using your generated graph for the first situation, describe how the unit rate of the amount of money paid monthly is related to the slope of the line.
Ans; The unit rate is same because in both payments are made monthly
d) Determine if each relationship represented in the table, graph, and equation represents a proportional or non- proportional situation
Ans; Each relationship represented in the table , graph and equation is not proportional because it doesn't cross the origin.
What do you add to the cost of one frozen yogurt to get the cost of two frozen yogurt?
Answer:
You add another Frozen yogurt...
Answer:
You just add it again or multiply it by 2.
Step-by-step explanation:
For example, if the frozen yogurt cost $3.50, you would add it again or multiply it by 2. 3.50 + 3.50 = $7.00
A Pringles chip can has a diameter of about 2.8 inches and a height of about 11.8 inches (close to real measurement) what volume of air and chips can it hold ? Round your answer to the nearest hundredth
Answer:
72.66 in³
Step-by-step explanation:
The volume of a cylinder of radius r and height h is given by V = πr²h.
Here we have V = πr²h = π([2.8]/2 in)²(11.8 in) = π(1.96 in²)(11.8 in) = 23.1 π in³, or approximately 72.66 in³
ice, as long as it stays in its frozen form, will not lose its shape or its volume. Why?
solid form
Step-by-step explanation:
it will not loose shape because it is in solid form
Answer:
It freezes it self in the solid state
Step-by-step explanation:
Area = 27 mi2
The area of the polygon is 27 mi? What is the length of side
miles
Answer:
3 mi
Step-by-step explanation:
There are three squares with side a
The area of a square is s^2 where s is the side length
A of the square is a^2
We have three of them so add the areas together
a^2+a^2+a^2 = 3a^2
This is equal to 27
3a^2 = 27
Divide each side by 3
3/3a^2 = 27/3
a^2 = 9
Take the square root of each side
sqrt(a^2) = sqrt(9)
a = 3
Identify Y, inscribed angels
Answer:
y = 2
Step-by-step explanation:
PQ is a diameter, so arc PQ has a central angle of 180°. Inscribed angle PRQ has a measure half that, or 90°. (An inscribed triangle with one side a diameter is a right triangle.)
Then you can write ...
53y -16 = 90
53y = 106 . . . . . add 16
y = 106/53 = 2 . . . . divide by the coefficient of y
y = 2
A catalog sales company promises to deliver orders placed on the Internet within 3 days. Follow-up calls to a few randomly selected customers show that a 95% confidence interval for the proportion of all orders that arrive on time is 70%±88%.
A. What does this mean? For each conclusion, state whether it is correct or not and explain why. Complete parts a through e below.
B. Between 62% and 78% of all orders arrive on time. State whether the conclusion is correct or not and explain why. Choose the correct answer below.
Answer:B. Between 62% and 78% of all orders arrive on time. State whether the conclusion is correct or not and explain why. Choose the correct answer below.
Step-by-step explanation:
A catalog sales company promises to deliver orders placed on the Internet within 3 days. Follow-up calls to a few randomly selected customers show that a 90% confidence interval for the proportion of all orders that arrive on time is 89% ± 6%.
a) The correct answer is A
b) The correct answer is B
c) The correct answer is C
d) The correct answer is D.
e) The correct answer is B.
Here, we have,
a) Between 83% and 95% of all orders arrive on time.
The correct answer is A. This statement is correct.
b) 90% of all random samples of customers will show that 89% of orders arrive on time.
The correct answer is B. This statement is not correct. It implies certainty, but in reality, the statement refers to the confidence interval estimate for the proportion of orders that arrive on time based on the sample.
c) 90% of all random samples of customers will show that 83% to 95% of orders arrive on time.
The correct answer is C. This statement is not correct. No more than 95% of all orders arrive on time. The confidence interval represents the range within which the true proportion is estimated to fall, but it doesn't guarantee that all intervals will cover the true proportion.
d) The company is 90% sure that between 83% and 95% of the orders placed by the customers in this sample arrived on time.
The correct answer is D. This statement is not correct. The confidence interval provides an estimate of the proportion of orders that arrive on time, not a measure of the company's certainty.
e) On 90% of the days, between 83% and 95% of the orders will arrive on time.
The correct answer is B. This statement is not correct. It implies certainty about the proportion of orders arriving on time, but the confidence interval only provides an estimate based on the sample data and does not guarantee the exact proportion for every day.
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complete question:
A catalog sales company promises to deliver orders placed on the Internet within 3 days. Follow-up calls to a few randomly selected customers show that a 90% confidence interval for the proportion of all orders that arrive on time is 89% ± 6%. What does this mean? Are the conclusions below correct? Explain.
a) Between 83% and 95% of all orders arrive on time.
b)90% of all random samples of customers will show that 89% of orders arrive on time. c) 90% of all random samples of customers will show that 83% to 95% of orders arrive on time.
d) The company is 90% sure that between 83% and 95% of the orders placed by the customers in this sample arrived on time. e) On 90% of the days, between 83% and 95% of the orders will arrive on time.
a) Choose the correct answer below.
A. This statement is correct.
B. This statement is not correct. It implies certainty.
C. This statement is not correct. No more than 95% of all orders arrive on
D. This statement is not correct. At least 83% of all orders arrive on time.
how do u solve -10 + z - 1 = 7z - 5 ?
Answer:-1
Step-by-step explanation:
-10+z-1=7z-5
Collect like terms
7z-z=-10-1+5
6z=-6
Divide both sides by 6
6z/6=-6/6
z=-1
what is nine hundred seven thousands in decimal srandard form
Answer:
0.907
Step-by-step explanation:
0.000 thousandths place
Answer:
9.0 x 10⁶
Step-by-step explanation:
if your looking for 900,000
ONLY BOYS ANSWER PLSSSS
What would you do if Shakira was right next to you and you can do whatever you want to her :)
Answer:
you need Jesus lol :)
Step-by-step explanation:
.....
What is the disciminant of 3x^2-10x=-2
Answer:
76
Step-by-step explanation:
First get the equation into the form
ax^2 +bx+c =0
3x^2-10x+2=-2+2
3x^2-10x+2 =0
The discriminant is
b^2 -4ac where a=3 b = -10 c =2
(-10)^2 - 4(3)(2)
100 - 24
76
Junior bought a bag of mixed fruit snacks. The flavors in the bag are 4 strawberry, 3 cherry, and 5 grape. If he chooses one fruit snack at random, what it the probability of the first one being grape?
Answer:I believe it would be 5/12
Step-by-step explanation:
You add all of them up then since it's 5 grapes and in total there is 12 fruit snacks. It should be 5 grapes of 12 fruit snacks in the bag.
Walter’s family made a bowl of punch to have at their summer picnic. They used 1 ½ gallons of orange juice, 3 quarts of soda, 3 cups of lemonade, and 2 cups of cranberry juice. Would their 3 gallon punch bowl be big enough? How many cups away from 3 gallons are they?
Answer:
YES,30
Step-by-step explanation:
Can someone explain it to me please(? C:
I don’t know how to solve the problem when there’s two different variables next to each other.
Answer:
11
Step-by-step explanation:
just put the values in for the variables
5(3)(1) - 4(1)
15(1) - 4(1)
15 - 4
11
(Brainliest pleaseee)
Which mixes number is equivalent to the improper fraction 17/10
Answer:
1 7/10
Step-by-step explanation:
Your Welcome :)
Answer:
1 7/10
Step-by-step explanation:
17/10
To find the mixed number, we have to see how many times 10 goes into 17. (Only whole numbers)
17➡1*10 Remainder 7
Since there is a remainder seven we can put 7/10. Since 10 went once into 17 we can say the anwser is 1 7/10
1) Which system of linear equations could the graph represent? A) y = x + 5 y = 2x + 4 B) y = 3x + 6 y = −4x + 8 C) y = −3x + 6 y = −x + 3 D) y = −2x + 6 y = −4x + 8
Answer:
A
Step-by-step explanation:
Correct systems of linear equations which represent the two lines are,
a. x=3, y=6
e. y= x + 3, y= 2x
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
There are two lines are graphed on the same coordinate plane.
And, the lines only intersect at the point (3,6).
Now, We know that;
When Point (3, 6) is lies on line then it satisfy the equation of lines.
Hence, By options;
a. x=3, y=6
Clearly, Point (3, 6) is lies on line.
e. y= x + 3, y= 2x
y = x + 3
y = 3 + 3
y = 6
Hence, Point (3, 6) is lies on line.
Thus, Correct systems of linear equations which represent the two lines are,
a. x=3, y=6
e. y= x + 3, y= 2x
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complete question:
Two lines are graphed on the same coordinate plane.the lines only intersect at the point (3,6).which of these systems of linear equations could represent the two lines?
a. x=3
y=6
b. x=6+y
y=3+x
c. y=3x-3
y= x-1
d. x=3+y
y=6+x
e. y= x+3
y= 2x
what is (4 to the square root of 81)5?
Answer:
1310720
Step-by-step explanation:
Find out the frist part "4 to the square root of 81" 262144
then times it by 5
to get 1310720
Can y’all answer this or not !?
Answer:
b
Step-by-step explanation:
Answer:
x=417.6
Step-by-step explanation:
Let's solve your equation step-by-step.
0.5x+78.2=287
Step 1: Subtract 78.2 from both sides.
0.5x+78.2−78.2=287−78.2
0.5x=208.8
Step 2: Divide both sides by 0.5.
0.5x divided by 0.5
208.08 divided by 0.5
10^2What is the answer
Answer:
100
Step-by-step explanation:
10 times 10=100
Answer: 100
Step-by-step explanation: The 2 in this problem means that we are going to multiply 10 twice in order to find the answer.
When we multiply a number by itself, it's called squaring.
So any number squared is that number times itself.
So 10² is just 10 · 10 or 100.
