You build a cornhole game. The game is constructed from a sheet of plywood supported by two boards. The two
boards form a right angle and their lengths are 12 inches
and 46.5 inches. Please help!!
Answers
The length of side x of the pyramid is equal to 47 inches.
Given the following data:
Length A (adjacent) = 12 inches.Length B (opposite) = 46.5 inches.To determine the length of side x of the pyramid, we would apply Pythagorean's Theorem:
What is Pythagorean Theorem?Pythagorean theorem is a fundamental mathematical expression in Euclidean geometry that can be used to determine any of the three (3) sides of a right triangle.
Mathematically, Pythagorean's Theorem is given by this formula:
\(c^2 = a^2 + b^2\)
Where:
c is the hypotenuse.a is the adjacent side.b is the opposite side.Substituting the given parameters into the formula, we have:
\(x^2=2^2 +46.5^2\\\\x^2=4+2162.25\\\\x^2=2166.25\\\\x=\sqrt{2166.25}\)
x = 46.54 ≈ 47 inches.
b. To find the length of the support:
Since the support is altitude (y) to the hypotenuse of the right-angled triangle, we have:
Length = \(\frac{12 \times \sqrt{47}} {47}\)
Length = 1.75 ≈ 2 inches.
c. The support would attach to base of the hypotenuse of the plywood, which is the triangle formed by altitude (y) to the hypotenuse of the right-angled triangle.
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Related Questions
A large company event was held in a park on a hot day. Afterward, many of the employees got sick. Some blamed the potato salad. To investigate, a random sample of 20 sick employees and a random sample of 20 non-sick employees are selected. Each selected individual is asked if they ate the potato salad. The results are displayed in the table.
Management would like to know if there is convincing evidence that the distribution of responses about eating the potato salad differs for all employees who are sick versus those who are not sick. What are the appropriate hypotheses for this test?
H0: There is no difference in the distribution of responses among those who are and are not sick.
Ha: There is a difference in the distribution of responses among those who are and are not sick.
H0: There is a difference in the distribution of responses among those who are and are not sick.
Ha: There is no difference in the distribution of responses among those who are and are not sick.
H0: There is no difference in the distribution of responses for the 20 employees who are sick and the 20 employees who are not sick.
Ha: There is a difference in the distribution of responses for the 20 employees who are sick and the 20 employees who are not sick.
H0: There is a difference in the distribution of responses for the 20 employees who are sick and the 20 employees who are not sick.
Ha: There is no difference in the distribution of responses for the 20 employees who are sick and the 20 employees who are not sick.
Answers
The appropriate hypotheses for this test are: H0: There is no difference in the distribution of responses. Ha: There is a difference in the distribution of responses.
The chosen hypotheses are based on the objective of the investigation, which is to determine if there is convincing evidence that the distribution of responses about eating the potato salad differs between employees who are sick and those who are not sick.
The null hypothesis (H0) assumes that there is no difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This means that the proportion of employees who ate the potato salad would be the same in both groups, and any observed difference in the distribution of responses is due to random chance or factors unrelated to being sick or not sick.
On the other hand, the alternative hypothesis (Ha) proposes that there is a difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This suggests that the proportion of employees who ate the potato salad would be significantly different in the two groups, indicating a possible association between consuming the potato salad and getting sick.
By formulating these hypotheses, the investigation aims to evaluate whether the data provides convincing evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating a meaningful relationship between eating the potato salad and falling sick.
Therefore, the correct answer is:
H0: There is no difference in the distribution of responses about eating the potato salad among those who are and are not sick.
Ha: There is a difference in the distribution of responses about eating the potato salad among those who are and are not sick.
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If 6times a number is added to -3, then the results is equal to 9 times the number. Find the number
Answers
To determine the missing number:
\(\text{Let the missing number = x}\)\(\begin{gathered} 6\text{ times a number = 6x} \\ 6x+(-3)=9x \\ 6x-3=9x \end{gathered}\)collect like terms
\(\begin{gathered} 6x-9x=3 \\ -3x=3 \\ \text{divide both side by -3} \\ -\frac{3x}{-3}=\frac{3}{-3} \\ x=-1 \end{gathered}\)Therefore the missing number = -1
please hurry .The side of Mr. Miller’s barn has a length of 27 feet and an area of 656.1 square feet. How wide is the side of Mr. Miller’s barn?
Answers
Answer:
24.3
Step-by-step explanation:
area of a rectangle =length*width
if we know at least the 2 quantities already
total area = 656.1
and one of the sides = 27
we have to divide the are by one of the sides to get the remaining side
width = area/length
656.1 divided by 27 equals 24.3
Answer:
24.3 he was rii i got my answer frm here
Step-by-step explanation:
Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained:
y(hat)= 500 + 4x
Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is:
A.) $900
B.) $900,000
C.) $40,500
D.) $505,000
Answers
The point estimate for sales with an advertising spending of $10,000 is given as follows:
B.) $900,000.
What is defined by the linear regression equation?The linear regression equation for this problem is defined as follows:
y = 500 + 4x.
The variables for the equation are given as follows:
The variable x represents the advertising money spent, in hundreds of dollars.The variable y represents the sales, in thousands of dollars.If advertising is $10,000, the value of x is given as follows:
x = 10000/100 = 100.
(as each unit of x represents $100).
Thus the point estimate of the sales is obtained as follows:
y = 500 + 4(100) = 500 + 400 = 900.
As each unit of y is measured in thousands of dollars, the sales were of $900,000, meaning that the correct option is given by option B.
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What is the probability of landing a C, 4 when spinning these spinners at the same time?
Answers
Answer:21%
Step-by-step explanation:21%
A car travels 90 miles in 1.5 hours. How many miles will it travel in 5 hours if its speed remains the same?
Answers
Answer:
300 miles
Step-by-step explanation:
i am doing the same test right now
Help please answer really quick. I really need help. ( Math )
Answers
Answer:
0.25 lbs
ExplanationYou can translate the 1/2 a pound into 0.5lbs, which is equivalent. Then, this is the easier part. Sarah divides the clay into two equal pieces. This is asking you to halve 0.5lbs. The answer being 0.25lbs
Salma is inviting 10 friends to a party. Each friend wants 6 cookies
and each box has 10 cookies.
How many boxes should Salma get?
Answers
Answer:
salma needs 6boxes of cookies
Answer:
6 boxes
Step-by-step explanation:
if there are the 10 friends and each of them want 6 cookies that would be
10 x 6 =60
and if each box has 10 cookies then
60 ÷ 10 = 6
Please help ASAP questions and answer selection in screenshot
Answers
The domain of the function consists of all real numbers greater than 0.
What is a domain?A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
Next, we would determine the function which models the amount of gas as follows:
Function, f(x) = rate × x
Function, f(x) = 2.25 × x
Function, f(x) = 2.25x
Based on the function above, we can reasonably and logically deduce that the amount of gas cannot be negative. Therefore, the domain of this function is given by:
Domain = [0, ∞]
In conclusion, the domain is equal to all real numbers that are greater than zero (0).
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I really think it’s B ...Help?
Answers
Write an expression using the distributed property to dind the product of 7x63
Answers
The product of the expression 7 x 63 is 441.
We have,
To find the product of 7 x 63 using the distributive property, we can break down 63 as the sum of its factors, such as 60 and 3:
7 x 63 = 7 x (60 + 3)
Now, we can apply the distributive property by multiplying 7 to each term inside the parentheses:
7 x (60 + 3) = 7 x 60 + 7 x 3
Simplifying further:
7 x 60 + 7 x 3 = 420 + 21
Therefore,
The product of 7 x 63 is 441.
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Find two square numbers that total 45
Answers
x^2+^2=45
if ×=3 and y=6
then 9+36=45
A laptop computer is purchased for $2100. Each year, its value is 75% of its value the year before. After how many years will the laptop computer be worth$300 or less?
Answers
SOLUTION:
After the first year, the price of the laptop computer is;
\(P_1=0.75\times2100=1575\)After the second year, the price of the laptop computer is;
\(P_2=0.75\times1575=1181.25\)After the third year, the price of the laptop computer is;
\(P_3=0.75\times1181.25=885.94\)After the fourth year, the price of the laptop computer is;
\(P_4=0.75\times885.94=664.45\)After the fifth year, the price of the laptop computer is;
\(P_5=0.75\times664.45=498.34\)After the sixth year, the price of the laptop computer is;
\(P_6=0.75\times498.34=373.75\)After the seventh year, the price of the laptop computer is;
\(P_7=0.75\times373.75=280.32\)CORRECT ANSWER: 7 years
answer will mark brainly
Answers
Answer:
D(Angle A and Angle F)
Step-by-step explanation:
I marked them as abba and a is A and the other one was F which is D
Answer:
alternate angles are congruent angles. So, from figure it is clear that angle A and F are congruent. Also E and B are congruent. on other hand C & H also D and G
Step-by-step explanation:
In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, what would the same 30 second commercial have cost during the first Super Bowl in 1967, when the CPI was 33.4? Round your answer to the nearest hundred dollars.
Answers
In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.
To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).
The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.
Given data:
Cost of a 30-second commercial in 2021 = $5.6 million
CPI in 2021 = 271.4
CPI in 1967 = 33.4
To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:
Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)
Cost in 1967 = ($5.6 million) * (33.4 / 271.4)
Cost in 1967 ≈ $0.689 million
To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:
Cost in 1967 ≈ $68,900
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Change 0.12 to a ratio.
Answers
Answer:
3:25
Step-by-step explanation:
The photo shows how it's solved.
Answer: 3:25
Step-by-step explanation:
Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator
0.12 = 0.12/1
Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.
0.12 x 100
------------ = 12/100
1 x 100
Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)
12 ÷ 4
--------- = 3/25
100 ÷ 4
Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:
3
25 = 3:25
Expressed as a single fraction, 3/4x - 2/5x is equal to
Answers
The single fraction is 7x/20
What is a fraction?A fraction can be defined as the part of a whole variable, number or element.
The different types of fractions are;
Simple fractionsMixed fractionsProper fractionsComplex fractionsImproper fractionsWhat are algebraic expressions?Algebraic expressions are mathematical expressions consisting of terms, coefficients, variables, factors and constants.
They are made of operations such as multiplication, addition, subtraction, division, etc
Given the expression;
3/4x - 2/5x
Find the LCM
15x - 8x/20
7x/20
Thus, the value is 7x/20
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Translate this phrase into an algebraic expression.
Five more than the product of 11 and a number
Use the variable n to represent the unknown number.
Answers
Answer:
5+(11 x n)
Step-by-step explanation:
I hope this helps
6 + 4|2x + 6| = 14
Solve for x
Answers
Answer:
x = -1
Step-by-step explanation:
6+4 = 10
14-10 = 4
2x + 6 = 4
2x (-2) = -2
-2 + 6 = 4
divide the polynomials x^2-10,000/x-100
Answers
Answer:
x+100
Step-by-step explanation:
x^2-10,000/x-100
x^2-10000 is a difference in squares and can be factored.
x^2-10000 = (x+100)(×-100).
(x+100)(x-100)/(x-100)
(x-100) cancel each other.
x+100 remains.
the width of a rectangle is half as long as the length. the rectangle has an area of 72 square feet. what are the length and width of the rectangle
Answers
Answer:
w-6 l-12
Step-by-step explanation:
Let's put this into a system of equations.
w=0.5L
wL=72
Let's plug in the w value in the second equation.
0.5L(L)=72
L²=144
L=12
Now we plug our L value into the first equation.
w=1/2(12)
w=6
The width is 6 and the length is 12.
Answer the equation
34 − 4b = 14
b = ?
Answers
Answer:
b = 5
Step-by-step explanation:
Answer:
b = 5
Step-by-step explanation:
34-4b = 14
Subtract 34 from both sides of the equation,
-4b = 14-34
-4b = -20
Divide both sides of the equation by -4,
b = 5
The accompanying technology output was obtained by using the paired data consisting of foot lengths (cm) and heights (cm) of a sample of 40 people. Along with the paired sample data, the technology was also given a foot length of 20.4cm to be used for predicting height. The technology found that there is a linear correlation between height and foot length. If someone has a foot length of 20.4 cm, what is the single value that is the best-predicted height for that person?
Answers
The best-predicted height for someone with a foot length of 20.4 cm is approximately 65.83 cm.
To find the best-predicted height for someone with a foot length of 20.4 cm, we need to use the linear regression equation that relates foot length and height. The linear regression equation is of the form:
y = a + bx
where y is the predicted height, x is the foot length, a is the y-intercept, and b is the slope of the regression line.
From the given information, we know that the technology found a linear correlation between height and foot length. This means that we can use the paired data to calculate the values of a and b in the regression equation.
Using the paired data and technology, we can obtain the following regression equation:
height = 34.774 + 1.4966 (foot length)
Now we can substitute the given foot length of 20.4 cm into the equation to obtain the predicted height:
height = 34.774 + 1.4966 (20.4)
height = 65.83 cm
Therefore, the best-predicted height for someone with a foot length of 20.4 cm is approximately 65.83 cm.
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A car rents for $280 per week plus $0.15 per mile. Find the rental cost for a three-week trip of 900 miles.
Answers
Answer:
$975
Step-by-step explanation:
The car is rented for 3 weeks
the rent is for a week is $280 so for three weeks it would be
3*28 = $840
now we need to add the per mile price to this
1 mile = $0.15 for 900 miles it would be
900*(0.15) = 135
So the total rental cost is
$840 + $135 = $975
What is the area of the following circle?
Correct answers only
Will mark brainlist
Answers
What is a ratio equivalent to 3:4 ? 3/4 2/3 4/3
Answers
Use the slip and y-intercept to identify the equation of this line
Answers
Answer:
y=2x
Step-by-step explanation:
equation formula is y=mx+b
m is slope
b is y-intercept
you know that slope is 2
y intercept is 0
so plug it into the equation
y=2x+0 or just y=2x
NEED HELP ASAP
The formula for the simple interest, I, is I=prt where p is principal, r is the annual interest rate, and t is the time elapsed in years.
A) solve the formula for r.
B) use the equation you just found to determine the annual interest rate on an account that earned $125.00 in simple interest after 6 months with principal deposit of $5.000.00.
Answers
A) Formula for r is r = I/p*t
B) The annual interest rate on the account is 0.05%
Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal and by the number of days that elapse between payments.
For part A of the question, I=p*r*t
Therefore, r = I/p*t ( by taking interest rate on one side and moving rest of the terms on the other side of the 'equals to'. As we know that when we move a term which is being multiplied on one side to the other side, it is then used as a divisor.)
For part B of the question, put values in the above formula
simple interest earned = $125,00
principal deposit = $5,000,00
time period in years = 6 months that is 1/2 years
r = I/p*t
r = 125,00/5,000,00*1/2
r = 0.05%
Therefore, The formula solved for r is r = I/p*t and the annual interest rate on the account that earned $125,00 in simple interest after 6 months with principal deposit of $5,000,00 is 0.05%.
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Which of the following are consistent with the
guidelines for hitching trailers?
Trailers must be connected to the tow vehicle before loading.
Loads cannot exceed the maximum payload of 1,750 pounds.
Loads cannot exceed the maximum payload of 3,000 pounds.
Customer vehicles must have at least a frame mounted Class 3 receiver hitch
with a 2" or 2 5/6" ball.
Answers
The statement that are consistent with the guidelines for hitching trailers are:
A. Trailers must be connected to the tow vehicle before loading.
D. Customer vehicles must have at least a frame mounted Class 3 receiver hitch with a 2" or 2 5/6" ball.
Guidelines for hitching trailers?Option A: Because it guarantees that the weight of the cargo is evenly distributed and attached to the trailer before the vehicle is driven this recommendation is consistent with safe hitching techniques.
Option D: Because it guarantees that the trailer is securely fastened to the tow vehicle and can support the weight of the cargo this recommendation is consistent with safe hitching techniques. A 2" or 2 5/16" ball ensures the trailer is firmly fastened to the hitch and a Class 3 hitch is made to support the weight of heavier trailers.
Therefore the correct option is A and D.
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What is the sale price to the nearest cent? $239 television; 10% discount
Answers
Answer:
The sale price will be: $215.10
Step-by-step explanation:
We know that:
Sale price = Regular price × (100% - Discount %)
= Regular price × (100% - 10%)
= 239 × 90%
= 239 × 0.9
= 215. 10 $
Therefore, the sale price will be: $215. 10