The surface area of the triangular prism be 108 ft²
The volume of the triangular prism be 48 ft³.
Given, a triangular prism (base is a right triangle).
Triangle legs are 3 ft and 4 ft, hypotenuse is 5 ft, height of prism is 8 ft.
Now, the surface area of the triangular prism is,
Surface Area = 2×Area of the base triangle + Side rectangle 1 +Side rectangle 2 + Side rectangle 3
Surface Area = 2×(1/2×3×4) + 5×8 + 3×8 + 4×8
Surface Area = 12 + 40 + 24 + 32
Surface Area = 108 ft²
Now, Volume of the triangular prism be,
Volume = Area of the base triangle × height
Volume = 1/2×3×4×8
Volume = 48 ft³
Hence, the surface area of the triangular prism be 108 ft²
and the volume of the triangular prism be 48 ft³.
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A vending machine i deigned to dipene a mean of 7. 5 oz of coffee into an 8-oz cup. If the tandard deviation of the amount of coffee dipened i 0. 5 oz and the amount i normally ditributed, find the percent of time the machine will dipene le than 7. 75 oz
The percent of times the machine will dispense less than 7.75 oz. is 69.15%.
In the given question we have to find the percent of time the machine will dispene less than 7.75 oz.
A vending machine we deigned to dipene a mean of 7.5 oz of coffee into an 8-oz cup.
If the standard deviation of the amount of coffee dipened is 0.5 oz and the amount is normally ditributed.
Mean = 7.5 ,
Standard Deviation = 0.5
P(z< 7.5) = P(z<(X-Mean)/Standard Deviation)
P(z< 7.5) = P(z<(7.75-7.5)/0.5)
P(z< 7.5) = P(z<0.25/0.5)
P(z< 7.5) = P(z< 0.5)
P(z< 7.5) = 0.6915
P(z< 7.5) = 69.15%
Hence, the percent of times the machine will dispense less than 7.75 oz. is 69.15%.
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Austin is blocking off several rooms in a hotel for guests coming to his wedding. The hotel can reserve small rooms that can hold 2 people, and large rooms that can hold 3 people. Austin booked a total of 22 rooms which can accommodate 53 guests altogether. Determine the number of small rooms reserved and the number of large rooms reserved.
Answer:
There are 13 small rooms and 9 large rooms reserved.
Step-by-step explanation:
First, we can make a system of equations. We can use s to represent the number of small rooms and l to represent the number of large rooms.
2 guests per small room added to 3 guests per large room equals 53 guests total, so 2s + 3l = 53.
The number of small rooms (s) plus the number of large rooms (l) equals the total number of rooms, so s + l = 22 or s = 22 - l.
We can substitute the first second equation into the first equation.
2 (22 - l) + 3l = 53
44 - 2l + 3l = 53
l = 9
So, the number of large rooms is 9. Then, to find the number of small rooms, we can substitute l into the second equation.
s = 22 - 9
s = 13
So, the number of small rooms is 13.
ANSWER ASAP 8TH GRADE MATH EASY
Answer:
It is the first option
Step-by-step explanation:
Alyssa works 6.4-hour shifts at the donut shop each day. Last week she earned $480 for working 32 hours. Describe the unit rate in this problem.
The unit rate for this problem is how much Alyssa earns per hour
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Alyssa works 6.4-hour shifts at the donut shop each day.
Last week she earned $480 for working 32 hours.
Now, To determine her earnings per hour we have to divide her total earnings by the total no. of hours she worked which is,
= $(480/32).
= $15 per hour.
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Select the correct answer.
What is the equation of the line that has a slope of 3 and goes through the point (-3,-5)?
A. y = 3x + 4
B. y = 3x − 14
C. y = 3x − 4
D. y = 3x + 12
(It is not y = 3x - 4 OR C)
100 points if you answer this correctly
Since triangle P'Q'R' is the result of a transformation of triangle PQR, an algebraic representation which best describes this transformation is: C. (x, y) → (5x/2, 5y/2).
What is a transformation?In Mathematics, a transformation can be defined as the movement of a point from its original (initial) position to a final (new) location. This ultimately implies that, when an object is transformed, all of its points would be transformed as well.
From the information provided above, we can logically deduce the following coordinates:
Point P = (-1, 1)Point Q = (2, 0)Point R = (-1, -2)Point P' = (-5/2, 5/2)Point Q' = (5, 0)Point R' = (--5/2, -5)Therefore, the transformation rule is given by:
P (x, y) → P' (x, y)
Point P = (-1, 1) → Point P' = ((5/2 × -1), (5/2 × 1)) = Point P' = (-5/2, 5/2).
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someone please help me.
72/6 = 12
Write a situation for this equation and draw a picture that goes with it.
The picture for the condition is attached below.
What is factors of number?
A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics. As an illustration, 3 and 6 are factors of 12 because 12 3 = 4 and 12 6 = 2, respectively. 1, 2, 4, and 12 are the other components that make up 12.
Let, the factors of 72 are
72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24 36, 72.
When we divide 72 by 6 we get 12.
⇒ [tex]\frac{72}{6} = 12[/tex]
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It takes 5 minutes for your printer to print 40 papers
How long does it take for your printer to print 12 papers?
It will take 1.5 minutes for printer to print 12 papers.
Given,
Time taken to print 40 papers=5 minutes
then,
Time taken to print 1 paper =[tex]\frac{5}{40}=\frac{1}{8}[/tex] minutes
then to find time taken to print 12 papers, multiply 12
Time taken to print 12 paper,
[tex]Time=\frac{1}{8}*12\\\\Time=1.5\ minutes[/tex]
Thus, it will take 1.5 minutes for printer to print 12 papers.
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2 ft
2 ft
5 ft
4 ft
4 ft
2 ft
2 ft
Answer:
22ft
Step-by-step explanation:
2+2+5+4+4+2+2= 22
The base of the parallelogram has a length
of 10 cm. What is the height?
10 cm
12cm
14cm
The height is either 10 cm,12 cm,14 cm.
Given:
The base of the parallelogram has a length of 10 cm.
Here area is not given so the height may be anything.
suppose h = 10
area = base * height
= 10 * 10
= 100 cm^2
if h = 12
area = 10 * 12
= 120 cm^2
if h = 14
area = 10 * 14
= 140 cm^2
Therefore the height is either 10 cm,12 cm,14 cm.
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Determine the equation of the line that is parallel to the given line, through the given point
y = -5x + 1 ; (-2,3)
The equation of the line that is parallel to the given line, through the given point is y = -5x - 7
Given equation,
y = -5x + 1
Slope = m
= -5
For two lines to be parallel, slope is equal.
Therefore, m = -5 for another line.
Let the equation of the line be y = mx + c
This line passes through A(-2,3)
Therefore, 3 = -5(-2) + c
3 = 10 + c
c = 3 - 10
= -7
Hence, equation of line is y = -5x - 7.
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what is the answer to this
-1 39/45
that is the answer
At the penalty apr rate of 28. 99% and a balance of about $1800, approximately how much interest would you owe in one month?.
The interest rate for one month is 2.42% and the interest amount is $40 approximately.
Given,
The penalty APR rate = 28.99%
Balance amount = $1800
We have to find the interest for one month;
Here,
The APR of 28.99% is the yearly interest. To find the monthly rate:
= Rate / 12 months
= 28.99% / 12
= 2.42%
The amount owed is therefore;
= 1,800 x 2.42%
= $43.56
= $40.00 approximately
That is,
The interest rate for one month is 2.42% and the interest amount is $40 approximately.
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v - 10 + k³ when v = -2 and k = -3
-2 - 10 + (-3)^3
= -12 - 27
= -39
Answer:
-39
Step-by-step explanation:
Substitute v and k
v - 10 + k³
-2 - 10 -3³
Multiply the 3 and the power of thirds together
-2 -10 + 27
Combine like terms
Ms. Fraser’s total monthly cell phone bill this month was
$56.70. Her phone company charges $45.60 for unlimited
minutes and $0.10 for every text message sent.
Answer:
She sent 111 texts that month
Step-by-step explanation:
7. The basketball team is selling hats and gloves. They will earn $10 for every hat they sell and $8 for every pair of gloves. They want to sell a total of 40 items. Create two unique equations that model the number of hats, h, and the number of gloves, y, that the team is selling.
Answer:
5h+35y=390$
20h+20y=360$
Step-by-step explanation:
there are many answers possible.
The following are just examples:
5h+35y=390$
20h+20y=360$
a) Work out (5 × 10³) × (9 × 10')
Give your answer in standard form.
b) Work out (7 × 105) + (2 × 10²)
Give your answer in standard form.
Find the length x.
HELPPP PLSSSS
Answer: My answer is 4. You may want another answer.
Step-by-step explanation:
visual studying
what is 1 divided by [tex]\frac{1}{2}[/tex]?
Which is a solution set for |x + 3| = 6?
{-3, 3}
{-9,3}
{-6, 9}
The values of x in the given equation are x = -9 and x = 3. The solution set is [-9, 3]
Solving for the values of x in an equationFrom the question, we are to determine the value of x in the given equation.
The given equation is
|x + 3|= 6
Then, we can write that
x + 3 = 6 and -(x + 3) = 6
Solving the first equation
x + 3 = 6
Subtract 3 from both sides of the equation
x + 3 - 3 = 6 - 3
x = 3
Solving the second equation
-(x + 3) = 6
-x - 3 = 6
Add 3 to both sides of the equation
-x - 3 + 3 = 6 + 3
-x = 9
Multiply both sides of the equation by -1
-1 × -x = -1 × 9
x = -9
Hence, the solutions are x = -9 and x = 3
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a random sample of 1000 people was taken. four hundred fifty of the people in the sample favored candidate a. what is the upper limit for a 95% confidence interval for the true proportion of people who favored candidate a? round your answer to three decimal places.
The 95% confidence interval for the true proportion of people who favored candidate a is 0.419, 0.481
How to calculate confidence interval?
First, calculate sample proportion by divide number people who favored candidate by number of sample. So:
[tex]\pi[/tex] = 450 / 1,000 = 0.45
Then we use the formula for confidence interval
[tex]\pi[/tex] ± [tex]z\sqrt{\frac{\pi (1-\pi )}{n}}[/tex]
In which z is z score that has a p value of [tex]1 - \frac{\alpha }{2}[/tex]
For 95% confidence interval z is the value of Z that has a p value of [tex]1 - \frac{0.05}{2}[/tex] = 0.975, so z = 1.96
After we have [tex]\pi[/tex] value and z value then put it in the formula. So:
= 0.45 ± [tex]1.96\sqrt{\frac{0.45(1-0.45)}{1000} }[/tex]
= 0.45 ± 0.0308
= 0.419, 0.481
Thus, the 95% confidence interval for the true proportion of people who favored candidate a is 0.419, 0.481
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Describe the relationship between <1 and <5
Angles 1 and 5 constitutes one of the pairs
Step-by-step explanation:
a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 400 gram setting. based on a 25 bag sample where the mean is 399 grams and the variance is 400, is there sufficient evidence at the 0.025 level that the bags are underfilled? assume the population distribution is approximately normal. find the value of the test statistic. round your answer to three decimal places.
Using the t test statistic, the value of the test statistic is 1.25.
In the given question we have to find the value of the test statistic.
A manufacturer of chocolate potato chips would like to know whether its bag filling machine works correctly at the 400 gram setting.
= 400
A 25 bag sample had a mean of 399 grams and the variance is 400.
There is sufficient evidence at the 0.025 level that the bags are underfilled.
Sample size(n) = 25
sample Mean = 399
Sample Variance = 400
Standard Deviation = √Sample Variance
Standard Deviation = √400
Standard Deviation = 20
Population Mean = 400
So , the null and alternative hypothesis are
H0 : μ = 400
Ha : μ < 400
Using the sample t test statistic
t = (Population Mean - Sample Mean)/(Standard Deviation/Sample size)
t = (400 - 399)/(20/25)
t = 1*25/20
t = 1.25
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Find x, y and z. ILL GIVE BRAINLIEST
Answer:
x = 30
y = 15
z = 150
Step-by-step explanation:
90°, 2x°, and x and supplementary.
Using this knowledge, we can form the equation:
2x° + 90° + x° = 180°
and solve for x.
3x°+ 90° = 180°
3x° = 90°
x° = 30°
x = 30
x and z are same side interior angles. Therefore, they are supplementary.
Using this knowledge, we can form the equation:
x° + z° = 180°
30° + z° = 180°
z° = 150°
z = 150
z° and 2y° are supplementary.
Using this knowledge, we can form the equation:
z° + 2y° = 180°
150° + 2y° = 180°
2y° = 30°
y° = 15°
y = 15
Answer:
I will be waiting for you to mark me brainlest pls
I need it to move to another rank plsssssssssssssssss
i need help pls
PLEASE GIVE ME THE CORRECT ANSWERS FOR ALL 3 PROBLEMS IM BEGGING
The values of the function when x = 3 are -10. -1 and -3, respectively
The values of the functionFunction 1
The equation of the function is given as
y = -4x + 2
We have the value of x to be 3
So, we have
y = -4 x 3 + 2
Evaluate
y = -10
Function 2
The graph represents the notation of the function
On the graph, we have the value of y to be -1, when x = 3
This means that
y = -1
Function 3
The table represents the notation of the function
On the table, we have the value of y to be -3, when x = 3
This means that
y = -3
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Solve for y:
-3 + 18iy = x + 9i
A) -3
B) 0.5
C) 2
D) 4
Answer:
Step-by-step explanation:
the pizza costs £6.40
this is 20% less than the original price.
what was the original price of the pizza?
Answer:
8
Step-by-step explanation:
Price : %
[tex]x[/tex] : 100
6.4 : 80 (Got 80 by 100 - 20)
Cross multiply
100*6.4 = 80[tex]x[/tex]
640 = 80[tex]x[/tex]
640/80 = [tex]x[/tex]
[tex]x[/tex] = 8
What statement about the graph is true?
The true statement about the graph is
It is a function with the domain {-6 < x < 0} and the range {0 ≤ y ≤ 5}.
What is range?The range refers to all possible value in the out put of a graph.
The out put is the y coordinate and the possible values here is within the interval
0 ≤ y ≤ 5
What is domain?The domain refers to all possible value in the input of a graph.
The input is the x coordinate and the possible values here is within the interval
-6 ≤ x ≤ 0
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What is the formula for Circumcentre?
There is no definite formula for calculation of circumcenter of a triangle but a process for calculation of circumcenter has been described here.
What is circumcenter of a triangle?
Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.
Let the coordinate of A, B, C [tex]\Delta[/tex] ABC be ([tex]x_1, y_1[/tex]), [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] respectively and let the coordinate of circumcenter of [tex]\Delta ABC[/tex] is (x, y)
We need to find the length of AB, BC and AC
The length will be obtained in terms of x and y
On solving the equations, we will obtain the value of x and y
The value of x and y is the required coordinate of the circumcenter.
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solve polynomial equations by factoring
2x³ + 12x² = 0
The value of x is -6 or 0 which is obtained by solving the giving equation using factoring.
What exactly is a polynomial equation? Polynomial equations are those created using exponents, coefficients, and variables. The greater of its possible exponents is referred to as the equation's degree.How can a polynomial equation be solved?Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. Factoring cannot always be used to solve polynomial problems.The original equations' answers are the solutions to the derived equations.Given equation: 2x³ + 12x² = 0
Solving this equation by factoring as follows:
2x³ + 12x² = 0
= 2x²(x+6) = 0
So, x + 6 = 0 or 2x² = 0
x = -6 or x = 0
Therefore, the value of x is -6 or 0 which is obtained by solving the giving equation using factoring.
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