From the information given about the square pyramid, the maximum base length of the building is 67.42 cm.
How do you determine the maximum side length?We are given the following details are:
Base = b
Slant height (l) = 5b
The lateral surface area is calculated using:
L = 2bl
So, we have:
L = 2 * b * 5b
Evaluate the product
L = 10b²
The total surface area is calculated using:
T = L + b²
So, we have:
T = 10b² + b²
Evaluate the sum
T = 11b²
Recall that the maximum surface area is 50,000 square feet
So, we have:
11b² = 50000
Divide both sides by 11
b² = 50000/11
Taking the square root of both sides, we have
b = 67.42
Hence, the maximum base length of the building is 67.42 cm
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PreCalc work, Need help writing piecewise functions with graphs. Giving brainliest
Answer:
f(x) = 2 for x < -2
f(x) = -2x + 11 for x > 3
A machine can pack 5000 articles in 24 hours.How long will 3 such machine take to pack the same number of articles
The time taken for 3 machines to pack 5000 articles is 8 hours.
What are word problems?Word problems are mathematical problems expressed completely in words.The given problem is the rate of work done kind of word problem.To solve a word problem, first, observe the data given in words and apply the basic algebraic operations.The basic algebraic operations are addition, subtraction, multiplication, and division.How long will 3 such machines take to pack 5000 articles?It is given that,
A machine can pack 5000 articles in 24 hours. I.e,
1 machine → 5000 articles → 24 hours
3 machines → 5000 articles → 24/3 hours
Thus, 3 of such machines can pack the same number of articles in
24 ÷ 3 = 8 hours.
Therefore, 3 of such machines take 8 hours to pack 5000 articles.
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The lengths of the sides of the right triangle above are a, 3, and c. What is a in terms of c?
The expression for a in terms of c is [tex]a^{2}= \sqrt{c^{2} -9}[/tex]. The correct option is the third option [tex]a^{2}= \sqrt{c^{2} -9}[/tex]
Pythagorean theoremFrom the question, we are to determine the expression for a in terms of c
In the given right triangle, we can write that
[tex]c^{2} = a^{2} +3^{2}[/tex] (Pythagorean theorem)
Thus,
[tex]c^{2} = a^{2} +9[/tex]
[tex]a^{2}= c^{2} -9[/tex]
[tex]a^{2}= \sqrt{c^{2} -9}[/tex]
Hence, the expression for a in terms of c is [tex]a^{2}= \sqrt{c^{2} -9}[/tex]. The correct option is the third option [tex]a^{2}= \sqrt{c^{2} -9}[/tex]
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An agriculture company is testing a new product that is designed to make plants grow taller. This can be thought of as a hypothesis test with the following hypotheses.
H0: The product does not change the height of the plant.
Ha: The product makes the plant grow taller.
Is the following an example of a type I or type II error?
The sample suggests that the product does not change the height of the plant, but it actually does make the plant grow taller.
It is an example of Type I error.
About Type I error
The rejection of a null hypothesis (H0) when it is actually true is a Type I error. It is represented by the following condition,
Failure to reject a null hypothesis when it is true that it is false which is a Type II error.
How is this an example of Type I error?
The given case's hypothesis is described as follows:
H₀: The product has no effect on the plant's height.
Hₐ: The substance causes the plant to enlarge.
The sample claims that the product causes the plant to grow taller, however in reality, it has no effect on the plant's height.
Therefore, the sample recommends rejecting the null hypothesis even though it is true. Consequently, a result, this error is a Type I error.
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which linear inequality is represented by the graph
Answer:
The correct awnser is A : )
Step-by-step explanation:
here is a polygon. draw a scaled copy of the polycon with scale factor 3
The scaled copy of the polygon is added as an attachment
How to draw the scaled copy?The complete question is added as an attachment
The coordinates of the polygon are
A = (-7, 6)
B = (-10, 8)
C = (-10, 10)
D = (-6, 10)
The scale factor is 3.
So, the rule of dilation is
(x, y) = (3x, 3y)
Using the above rule, we have:
A' = (-21, 18)
B' = (-30, 24)
C' = (-30, 30)
D' = (-18, 30)
See attachment for the scaled copy of the polygon
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order the decimales from leaste to gratest: 72.5, 73.943, 72.1, 73.77,
43.2 43.219 42.1 42.59
38.507 38.507 38.4 28.23 39.5
71.743 71.3 71.3 72.43 72.5
The decimals would be ordered as:
72.1, 72.5, 73.77, 73.943
42.1, 42.59, 43.2, 43.219
28.23, 38.4, 38.507, 38.507, 39.5
71.3, 71.3, 71.743, 72.43, 72.5
How to Order Decimals?To order decimals from the least to the greatest, first state the lowest value, then progress to the highest taking account of the figures that come immediately after each decimal point.
The decimals will be ordered as shown below:
72.1, 72.5, 73.77, 73.943
42.1, 42.59, 43.2, 43.219
28.23, 38.4, 38.507, 38.507, 39.5
71.3, 71.3, 71.743, 72.43, 72.5
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A lawn can be mowed by 8 people in 6 hours. If 3 people take the day off and do not help mow the grass, how many hours will it take to mow the lawn? Please show me how you figured this out.
A. 6 2/5
B. 9 3/5
C. 2 1/4
D. 5 1/2
If 3 people take the day off, they will need (9 + 3/5) hours to mow the lawn. The correct option is B.
How many hours will it take to mow the lawn?Let's say that each person works at a rate R.
8 people can mow the lawn in 6 hours, then we can write:
(8*R)*6 hours = 1 lawn.
Solving for R:
R = (1/48 lawns per hour).
If 3 people take the day off, then the lawn is mowed by 5 people in a time T, then we need to solve:
(5*R)*T = 1 lawn.
Replacing the value of R:
(5/48 lawns per hour)*T = 1 lawn.
Then we have:
T = (48/5) hours.
We can rewrite that as:
T = (45/5 + 3/5) hours
T = 9 + 3/5 hours.
Then we conclude that the correct option is B.
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Your friend is helping to raise money for a local charity by participating in a cartwheel-a-thon. Your
friend is 70 inches tall with your friend's arms raised in the air. Your friend is able to complete a
cartwheel in 15 seconds. The charity sponsor supplies a wristband to each participant to assist in
counting the number of cartwheels completed. The wristband is 4 inches from the end of your friend's
arm. Write a model for the height h (in inches) of the wristband as a function of the time (in minutes)
given that the wristband is at the highest point when ; = 0.
The equation for the height exists h = 31 sin((8π)t + π/2) + 35.
How can the height of the wristband be modeled?The model for the height can be emanated from the general formula of the sine function, then
y = A sin(Bt - C) + D
Maximum point = 70 - 4 = 66 at t = 0
Minimum point = 4
Amplitude, A = (66 - 4) ÷ 2 = 31
D = 4 + 31 = 35
At t = 0, we have;
66 = 31 × sin(B × 0 - C) + 35
31 = 31 × sin(- C)
sin(- C) = 1
C = -π/2
1 minute = 60 seconds
1 second = 1 minute/60
15 seconds = (15/60) minutes
Period = 15 seconds = 15/60 minutes
Period = 2π/B
Therefore, 15/60 = 2π/B
1/4 = 2π/B
B = 2π/(1/4) = 8π
y = Height of the function
Let h denote the height of the wristband.
The equation for the height exists h = 31 sin((8π)t + π/2) + 35.
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Find f(-3) for f(x) = 4(2)^x.
Answer:
1/2
Step-by-step explanation:
[tex]f( - 3) = 4 {(2)}^{ - 3} = \frac{1}{2} [/tex]
FRACTIONS
Equivalent fractions
Fill in the blank to make the two fractions equivalent.
blank over 30=4/5
The complete fraction is 24/30=4/5
How to create an equivalent fraction?The expression is given as:
blank over 30=4/5
Represent the blank with x.
So, we have:
x/30=4/5
Multiply both sides by 30
x = 30 * 4/5
Evaluate
x = 24
Substitute x = 24 in x/30=4/5
24/30=4/5
Hence, the complete fraction is 24/30=4/5
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Which point is on the graph of f(x) = 5*?
O A. (0, 5)
O B. (0, 0)
• C. (5, 1)
O D. (1, 5)
Answer is (1,5)
The point that is on the graph of the function [tex]F(x) = 5^x[/tex] is given by:
D. (1,5).
Which points are on the graph of the function?The function is defined by:
[tex]F(x) = 5^x[/tex]
When x = 0, [tex]F(x) = 5^0 = 1[/tex], hence point (0,1) is on the graph of the function.
When x = 1, [tex]F(x) = 5^1 = 5[/tex], hence point (1,5) is on the graph of the function, which means that option D is correct.
When x = 5, [tex]F(x) = 5^5 = 3125[/tex], hence point (5,3125) is on the graph of the function.
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Aaron wants to make All-Tournament Team for his high school
basketball team. He needs to average at least 24 points a game
to get selected for All-Tournament Team. They are playing 4
games, in the first 3 games he scored 30, 17, and 25 points.
Answer:24
Step-by-step explanation:
Answer:
Step-by-step explanation:
a rectangle has horizontal sides of 3 (x-2)ft and vertical sides of 4x-7+(-2x) ft finde the value of x so that the rectangle has a perimeter of 34 ft
Based on the given horizontal and vertical sides of a rectangle and its perimeter, the value of x in the expression is 6
Perimeter of rectanglePerimeter of rectangle = 2(length + width)
Perimeter of the rectangle = 34 ftLength of the rectangle = 3(x - 2) ft= 3x - 6
Width of the rectangle = 4x - 7 + (-2x)= 4x - 7 - 2x
= 2x - 7
Perimeter of rectangle = 2(length + width)
34 = 2{(3x - 6) + (2x - 7)}
34 = 2(3x - 6 + 2x - 7)
34 = 2(5x - 13)
34 = 10x - 26
34 + 26 = 10x
60 = 10x
x = 60/10
x = 6
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I need help with this slope
Answer:
Step-by-step explanation:
First, the y-intercept is -3 so from -3 the slop to the next point is 4/1.
Can someone answer this for me
The equation of the line in standard form is 6x - 7y = - 11
How to represent linear equation in standard form?The standard form for linear equations in two variables is Ax + By = C.
Therefore, using (-3, -1)(1 / 2, 2)
y = mx + b
where
m = slopeb = y-interceptHence,
m = 2 + 1 / 1 /2 + 3 = 6 / 7
Hence,
-1 = 6 / 7(-3) + b
- 1 = - 18 / 7 + b
-1 + 18 / 7 = b
b = -7 + 18/ 7
b = 11 / 7
Therefore,
y = 6 / 7 x + 11 / 7
Using the standard form,
6 / 7 x - y = - 11 / 7
6x - 7y = - 11
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The linear equation in standard form is:
6x - 7y = -11
Which is the last option.
How to get the equation of the line?
The line in slope-intercept form is written as:
y = a*x + b
We can see that the line passes through the points (-3, -1) and (1/2, 2), then the slope is:
[tex]a = \frac{2 - (-1)}{1/2 - (-3)} = \frac{3}{3.5} = \frac{6}{7}[/tex]
Then we can write:
y = (6/7)*x + b
To find the value of b, we use the first point. It means that when x = -3, the value of y is -1, then we get:
-1 = (6/7)*-3 + b
-1 + 18/7 = b
-7/7 + 18/7 = b
11/7 = b
Then the equation is:
y = (6/7)*x + 11/7
If we multiply both sides by 7 we get:
7y = 6x + 11
Now we move the term with "x" to the left:
7y - 6x = 11
That is the line in standard form.
If we multiply both sides by -1, we get the last option:
6x - 7y = -11
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F(x) =5^2x find the derivative of X
The derivative of the function [tex]f(x)=5^{2x}[/tex] is [tex]\frac{df}{dx} =2ln5(5^{2x})[/tex]
Finding the derivative of a functionThe derivative of a function f(x) is the ratio of the change in f(x) to the change in x
The given function is:
[tex]f(x)=5^{2x}[/tex]
Let u = 2x
Find the derivative of u. That is, du/dx
du/dx = 2
f(x) = 5^u
[tex]\frac{df}{du} =5^ulnu[/tex]
Using the chain rule of derivative
[tex]\frac{df}{dx}=\frac{df}{du} \times\frac{du}{dx}[/tex]
[tex]\frac{df}{dx} =5^uln5 \times 2\\\\\frac{df}{dx} =2ln5(5^{2x})[/tex]
The derivative of the function [tex]f(x)=5^{2x}[/tex] is [tex]\frac{df}{dx} =2ln5(5^{2x})[/tex]
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The solution to the inequality expression is x>5 and the correct representation is a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Inequality expressionInequality expressions are expression not separated by an equal sign
Given the following inequality expression
–3(2x – 5) < 5(2 – x)
Expand
-6x + 15 < 10 - 5x
Collect the like terms
-6x + 5x < 10 -15
-x < -5
x > 5
Hence the solution to the inequality expression is x>5 and the correct representation is a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
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find the value of x
a) 2:5=8:x
Step-by-step explanation:
solution:
given,
or, 2:5 = 8:x
or, 2/5 = 8/x [ changing into fraction form ]
or, 2x = 40 [ doing cross-multiplication ]
or, x = 20 [ dividing both sides with 2]
WILL GIVE BRAINLIEST!!! If [tex]\frac{a}{b} =2[/tex] what is the value of [tex]\frac{a}{a-b}[/tex]?
Could the answer be D) or is it C)?
A) -2
B) 1
C) 2
D) It cannot be determined from the given information
Considering the given proportion, the value of [tex]\frac{a}{a - b}[/tex] is:
C) 2
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The proportion between a and b is given by:
a/b = 2.
Then:
a = 2b.
The expression is:
[tex]\frac{a}{a - b} = \frac{2b}{2b - b} = \frac{2b}{b} = 2[/tex]
Hence option C is correct.
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what is 3495 x 30595
Multiplication of 3495 by 30595 is: 106,929,525.
MultiplicationMultiplication can be defined as the way of multiplying a number by another name.
Using a calculator to multiply 3495 by 30595.
Hence:
Multiplication= 3495×30595
Multiplication= 106,929,525
Therefore Multiplication of 3495 by 30595 is: 106,929,525.
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True or false? The graph represents a function.
5
O A. True
O B. False
If np>5 and nq>5, estimate P (at least 10) with n=13 and p=0.5 by using the normal distribution as approximation for the binomial distribution, if np, or nq,5, then state that the normal approximation is not suitable.
Using the normal distribution, the probability is given as follows:
[tex]P(X \geq 10) = 0.0485[/tex].
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution are:
p = 0.5, n = 13.
Hence the mean and the standard deviation are:
[tex]\mu = np = 13 \times 0.5 = 6.5[/tex].[tex]\sigma = \sqrt{np(1-p)} = \sqrt{13 \times 0.5 \times 0.5} = 1.8028[/tex]Using continuity correction, the desired probability is P(X > 9.5), which is one subtracted by the p-value of Z when X = 9.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9.5 - 6.5}{1.8028}[/tex]
Z = 1.66
Z = 1.66 has a p-value of 0.9515.
1 - 0.9515 = 0.0485, then:
[tex]P(X \geq 10) = 0.0485[/tex].
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root of polynomial function f(x)=(x-3)^4(x+6)^2
The following figure shows the entire graph of a relationship.
See attached!
The correct answer is Yes. The graph represents a function. The function given is: F(x) = y(-5). Note that the value of x is zero.
What is the graph of a function?A function's graph is the set of all points in the plane of the form (x, f(x)). The graph of f might similarly be defined as the graph of the equation y = f. (x).
Thus, the correct answer or function represented in the graph is f(x) = y(-5)
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What is the domain of the function given below
Answer:
c. [-1, infinity)
Step-by-step explanation:
the domain the interval or set of valid x values (while the range is the same for the valid y values).
what is the smallest value of x we see for the graph ?
for x values we need to look left and right.
and the more left the value, the smaller it is.
so, in other words, what is the left-most x value e can find ?
x = -1
that is the "starting point" of the function. there is no functional value for any smaller x.
and then clearly, the function goes on and on to the right without any boundary in sight. so, it keeps going to the right in all eternity, that means it goes to infinity.
therefore the answer.
keep in mind that "infinity" is not a number, only a concept. so, when writing "infinity" at an interval end, it is not included (and we use a round bracket).
A college graduate expects to earn a salary of $55,000 during the first year after graduation and receive a 3% raise every year after that. What is the total income he will have received after ten years?
Answer:
$73915.40
Step-by-step explanation:
→ Find the multiplier
( 3 + 100 ) ÷ 100 = 1.03
→ Multiply by principal amount and raise it to the power of years
55000 × 1.03¹⁰ = 73915.40
Answer: $630,513.36
Step-by-step explanation:
Making a Formula for His Salary on a Given YearLet's make a table of values to see how much he earns every year after graduation.
1 year -> $55,000
2 years -> 55,000 * 103% = $56,650
3 years -> 56,650 * 103% = 55000 * 103% * 103% = $58,349.50
4 years -> 58349.50 * 103% = 55,000 * 103% * 103% * 103% = 55000(1.03)³
Here, we see that every year, he gets 103% of what he got the previous year, which is also 1.03 times his previous salary.
We also see that we multiply 55000 by 1.03 three times in the fourth year, and two times in the third year. This means that we multiply 55000 by 1.03 n-1 times.
Using this, let's generalize this for n.
n years -> [tex]55000(1.03)^{n-1}[/tex]
Finding the Sum after Ten YearsWe are trying to find his total income after ten years, or the sum of his salary from year 1 to year 10. We can represent this in sigma notation like this
[tex]% Adjusted limits of summation$\displaystyle\sum_{n=1} ^{10} 55000(1.03)^{n-1}$[/tex]
This essentially translates to the sum of the first ten terms in the sequence [tex]55000(1.03)^{n-1}[/tex], starting at n=1.
Since this is a geometric sequence, or a sequence where we need to multiply by the same number to get to the next term, we can find the sum using the sum of geometric series formula. This formula is as follows:
[tex]S_n=a_1\frac{1-r^n}{1-r}[/tex]
where [tex]S_n[/tex] is the sum of the first n terms, [tex]a_1[/tex] is the first term, r is the common ratio, and n is the number of terms. In this question, [tex]S_n[/tex] is the total income after n years, [tex]a_1[/tex] is his salary after the first year, r is how much his salary increases by each year, and n is the number of years we are calculating the sum for.
[tex]a_1[/tex] -> 55000
r -> 1.03
n -> 10
Now that we have the values for each variable, let's plug them in and solve
[tex]S_{10}=55000(\frac{1-1.03^{10}}{1-1.03})\\S_{10}=630513.36[/tex]
The total income he will have received after ten years is $630,513.36.
How does the graph of g(x) = (x − 2)^3 + 6 compare to the parent function of f(x) = x^3?
A. g(x) is shifted 2 units to the right and 6 units down.
B. g(x) is shifted 2 units to the right and 6 units up.
C. g(x) is shifted 2 units to the left and 6 units down.
D. g(x) is shifted 6 units to the left and 2 units down.
Answer: B. g(x) is shifted 2 units to the right and 6 units up.
Step-by-step explanation:
See attached image.
w^14+w^16
what will be the answer pls help
Answer:
there shouldnt be an answer, they are not like terms, for a proper answer it would have to be like terms, for example:
x^2+x^2=2x^2
or
w^12+w^12=2w^12
they need to have the same exponent for addition to happen
Determine a limit for a piecewise function
The limit for the given piecewise function does not exist(DNE).
4th option is correct.
What is the limit of a function?In mathematics, limits are the points at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend heavily on limits, which are required to determine integrals, derivatives, and continuity. It is applied during the analysis process and always focuses on the function's behavior at a certain time.
Unique real numbers are limits in mathematics.
According to the question,
Left hand limit of the function= -5(3)+4 = -15+4 = -11
Right hand limit of the function= (3)(3)+2 = 11
As the left and right-hand limits are not equal. Thus, the limit of the function does not exist.
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