Rewriting the expression based on the information will be 72(1 + z/72).
How to explain the expressionIn order to transform 72 + z into a product based on 72, we can apply the distributive property of multiplication over addition. Essentially, this property maintains that:
a x (b + c) = a x b + a x c
By extension, we can create the following equation:
72 + z = 72 + 1 x z
In order to produce an equivalent expression as a multiple of 72 and another factor, we would then need to use the distributive rule once again:
72 + 1 x z = 72 x 1 + 72 x z/72
Simplification leads us to arrive at:
72 + z = 72(1 + z/72)
Our end result is expressed as a synthesis between 72 and the expression (1 + z/72), namely:
72(1 + z/72).
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Charlie saves $28.35 each month for 6 months. In the seventh month, he only saves $10.70.
How much money will Charlie have saved after 7 months?
Answer:
I think it is $139.30. But I'm not 100% sure
Step-by-step explanation:
In a survey of 2266 adults, 736 say they believe in UFOs. Construct a 90% confidence interval for the population proportion of adults who believe in UFOs. A 90% confidence interval for the population proportion is ( ?, ?).
(Round to three decimal places as needed.)
Part 2
Interpret your results. Choose the correct answer below.
A.
With 90% probability, the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval.
B.
The endpoints of the given confidence interval shows that 90% of adults believe in UFOs.
C.
With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
D.
With 90% confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
The 90% confidence interval for the population proportion of adults who believe in UFOs is (0.309, 0.339).
C. With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
To construct a 90% confidence interval for the population proportion of adults who believe in UFOs, we can use the formula:
Confidence Interval = Sample Proportion ± Margin of Error
First, we calculate the sample proportion:
Sample Proportion \(\hat{p}\) = Number of adults who believe in UFOs / Total number of adults surveyed = 736 / 2266 ≈ 0.324
Next, we need to calculate the margin of error.
Since we are dealing with a large sample size, we can use the formula for a 90% confidence interval:
Margin of Error\(= Z \times \sqrt{(\hat{p} \times (1 - \hat{p}) / n)}\)
Here, Z represents the z-value for a 90% confidence level, which corresponds to a z-value of 1.645. n represents the sample size.
Margin of Error\(= 1.645 \times \sqrt{(0.324 \times (1 - 0.324) / 2266)}\) ≈ 0.015
Finally, we can construct the confidence interval:
Confidence Interval = 0.324 ± 0.015 = (0.309, 0.339)
Therefore, the 90% confidence interval for the population proportion of adults who believe in UFOs is (0.309, 0.339).
Now, let's interpret the results.
The correct answer is:
C. With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
This means that we are 90% confident that the true proportion of adults who believe in UFOs falls within the range of 0.309 to 0.339.
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What type of observation is this?
The cheese looks furry.
Answer:
This is a qualitative observation
Step-by-step explanation:
It is observing the qualities of the cheese as opposed to quantity which would include numbers or data.
Graph the equation y = |x| +5. Let x = -3, -2, -1, 0, 1,
2, and 3.
X
Find the following y-values. Then choose the correct
graph of the equation to the right.
y
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The graph of the equation y = |x| + 5 is given below.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
The given equation is y = |x| + 5.
Set the given values for x and find the corresponding values of y.
When x = -3, y = |-3| + 5 = 8
When x = -2, y = |-2| + 5 = 7
When x = -1, y = |-1| + 5 = 6
When x = 0, y = |0| + 5 = 5
When x = 1, y = |1| + 5 = 6
When x = 2, y = |2| + 5 = 7
When x = 3, y = |3| + 5 = 8
Graph of the equation is given below.
Hence the graph of the equation is found.
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What’s the answer to If =3+23
, what is
when =1
and =2
?
The value of y when a = 1 and b = 2 is 22.
How to solve an equation?The equation of can be solved as follows: We will substitute the value of a and b in the equation to find the value of y.
Therefore,
y = 3ab + 2b³
Let's find y when a = 1 and b = 2
Hence,
y = 3(1)(2) + 2(2)³
y = 6 + 2(8)
y = 22
Therefore,
y = 22
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Alguien que me explique como se saca la integral de este:
The integral distributes over the sum:
\(\displaystyle \int \left(4x^{\frac34} + 2x^{\frac34} + 4x^{\frac12} + 2x + 2\right) \, dx \\\\\\ = \int 4x^{\frac34} \, dx + \int 2x^{\frac34} \, dx + \int 4x^{\frac12} \, dx + \int 2x \, dx + \int 2 \, dx\)
Then just integrate each term using the power rule; if n ≠ -1, then
\(\displaystyle \int x^n \, dx = \frac{x^{n+1}}{n+1} + C\)
Then your integral is simply
\(\displaystyle \int \left(4x^{\frac34} + 2x^{\frac34} + 4x^{\frac12} + 2x + 2\right) \, dx \\\\\\ = \frac{4x^{\frac34+1}}{\frac34+1} + \frac{2x^{\frac34+1}}{\frac34+1} + \frac{4x^{\frac12+1}}{\frac12+1} + \frac{2x^2}2 + \frac{2x^1}1 + C \\\\\\ = \frac{16}7 x^{\frac74} + \frac87 x^{\frac74} + \frac83 x^{\frac32} + x^2 + 2x + C \\\\\\ = \boxed{\frac{24}7 x^{\frac74} + \frac83 x^{\frac32} + x^2 + 2x + C}\)
The table shows the number of free throws a player makes in a basketball game and the number of points the player scores in the game.
Number of free throws vs. Number of Points Scored
Number of free Throws Made (f) | Numbers of Points Scored (s)
5 15
3 11
8 20
7 18
9 21
Alex used a regression calculator to find the equation of the trend line y = a x + b for the data in the table. He rounded the values for a and b on his calculator as shown below.
a = 1.7
b = 6.2
Which trend line compares the data in the table?
s = 1.7 f + 6.2
s = 6.2 f + 1.7
f = 1.7 s + 6.2
f = 6.2 s + 1.7
Answer:
The regression equation of the data will be:
\(s=6.2f+1.7\)
Step-by-step explanation:
A simple linear regression equation is used to estimate the value of the dependent variable based upon the independent variable.
The general form of a simple linear regression equation is:
\(y=a+bx\)
Here,
y = dependent variable
x = independent variable
a = intercept
b = slope
The data is provided for the number of free throws a player makes in a basketball game and the number of points the player scores in the game.
The free throw in a basketball game implies that for every throw shot made the player receives point.
This implies that the points scored are based upon the number of free throws made by a player.
So, the dependent variable is the number of points scored and the independent variable is the number of free throws a player makes.
Then the regression equation of the data will be:
\(s=6.2f+1.7\)
Answer:
y = 1.7x + 6.2
Step-by-step explanation:
read the problem closely to figure out S and F. I can guarentee that if you read the entire thing, you will know if the answer is. It is either choice one or three
Ms. Chung drives the same distance to go to work every Monday through Friday. On Saturday she drove g the distance she drives to work. The distance she drove on Saturday was 0.9 miles. Part A: In the first box, enter an equation to represent the distance, d, that Ms. Chung drives to work. Part B: In the second box, enter the distance Ms. Chung drives to work.
A) The algebraic expression will be 12d + 7 = 91
B) He drives 7 miles per day to work.
For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.
The distance she drove on Saturday was; 0.9 miles.
The number of miles she drives per day:
84 miles/12
= 7 miles per day
Let the number of miles she travels be day = d
12d + 7 = 91 miles
12d + 7 = 91
12d = 91 - 7
12d = 84
d = 84/12
d = 7 miles per day
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Pat earns $489 per week at her new job. Calculate her annual salary. (Do not enter $ or comma in your answer.)
Answer:
25,428 this was a peice of pie
Step-by-step explanation:
The concerns about the impact of technology on our lives are growing. There have been
recent research reports about the negative impact of digital technology usage on stress,
work productivity, happiness, and overall well-being. In light of these concerns, a polling
organization asked technology experts about their opinion on our digital life and found
that 29% of the experts believe that in the future our lives will be more harmed than
helped by their digital environment. In an effort to confirm these results, a local tech
company decides to ask 215 randomly selected customers their opinions about their
digital life. Answer parts a through c below.
A
a. What is the probability that 35 or more people from this sample are concerned about
the digital environment?
The probability is
(Round to four decimal places as needed.)
The probability that 35 or more people from the sample of 215 customers are concerned about the digital environment is 0.7043.
To calculate the probability that 35 or more people from the sample of 215 customers are concerned about the digital environment, we can use the binomial distribution formula.
The binomial distribution is applicable here because we have a fixed sample size (215 customers) and each customer can be categorized as either concerned or not concerned.
Let's denote p as the probability that a randomly selected customer is concerned about the digital environment.
From the given information, we know that 29% of technology experts believe our lives will be more harmed than helped, so p = 0.29.
The formula for the probability mass function of the binomial distribution is:
\(P(X = k) = C(n, k) \times p^k \times (1 - p)^{(n - k)\)
Where:
P(X = k) is the probability of k successes (in this case, customers concerned about the digital environment)
C(n, k) is the number of combinations of n items taken k at a time
\(p^k\) is the probability of k successes
\((1 - p)^{(n - k)\) is the probability of (n - k) failures
Now, let's calculate the probability of having 35 or more customers concerned:
P(X ≥ 35) = P(X = 35) + P(X = 36) + ... + P(X = 215)
Using this formula, we can calculate the probability using a cumulative approach:
P(X ≥ 35) = 1 - P(X ≤ 34)
Calculating this probability requires summing up a large number of individual probabilities, which can be time-consuming.
Therefore, it is more practical to use statistical software or calculators to obtain an accurate answer.
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1/2 (2x + 5) = 3/4 (x + 1) + 5/2 show your work!!:)
Answer: 0
Step-by-step explanation:
1/2(2x+5)=3/4(x+1)+5/2
distribute 1/2 to 2x and 5
distribute 3/4 to x and 1
1/4x+5/2=5/2
subtract 5/2 to 5/2
1/4=0
multiply 1/4 by the reciprocal
4/1*1/4=0*4/1
Answer= 0
The equation z = 30x represents a(n) _____ variation.
a. direct
b. joint
c. inverse
d. combined
The equation z = 30x represents a direct variation the two variables, z and x, are directly proportional to each other. a.
Direct variation can be defined as a relationship between two variables where their values increase or decrease at the same rate.
In the case of the given equation, as x increases, z also increases proportionally.
Similarly, if x decreases, z will also decrease proportionally.
Direct variation can be represented as y = kx, where y and x are the variables, and k is the constant of variation.
In the given equation, we can see that z is the dependent variable, and x is the independent variable.
We can rewrite the equation as z = kx, where k = 30.
To understand how direct variation works, let's consider an example. Suppose we have an equation y = 5x, where y represents the cost of buying x apples at $5 per apple.
Here, the cost of buying apples is directly proportional to the number of apples purchased.
For instance, if we buy 10 apples, the total cost will be 10 × $5 = $50.
Similarly, if we buy 20 apples, the total cost will be 20 × $5 = $100.
Thus, we can see that the cost increases as the number of apples purchased increases, and vice versa.
The given equation z = 30x represents a direct variation is a type of relationship between two variables where their values increase or decrease proportionally.
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Show that the angle bisector of an equilateral triangle is perpendicular to the base
To show that the angle bisector of an equilateral triangle is perpendicular to the base, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.
How to prove that the angle bisector is perpendicular to baseAfter getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.
We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.
Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.
Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.
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WILL GIVE BRAINLIST IF CORRECT!!
The diameter of a red blood cell is about 0.0008 cm. The diameter of a whooping cough virus is about 2.5 x 10-5 cm. What is the approximate ratio of the diameter of the red blood cell to the diameter of the whooping cough virus? LOOK AT PICTURE
A.) 3.2 × 10^1
B.) 3.1 × 10^-3
C.) 3.1 x 10^-2
D.) 3.2 × 10^2
Answer:
b
Step-by-step explanation:
as 2.5 × 10-^5 is 250000 and b is 3100 and if you do 10-5 + 10-3 it is 10-8 which will give u 0.0008cm I think if my calculations r correct
Answer:
a
Step-by-step explanation:
just did it and got right
Find the reference angle
The reference angles of -320 is 40 degrees and the reference angle of 19π/12 is 5π/12
Finding the reference anglesFrom the question, we have the following parameters that can be used in our computation:
Angle = -320
The reference angle is caculated as
Reference = 360 + Angle
So, we have
Reference = 360 - 320
Evaluate
Reference = 40
For the other angle, we have
θ = 19π/12
The above angle is in the fourth quadrant
So, we subtract it from 2π to calculate the reference angle
Using the above as a guide, we have the following:
Reference angle = 2π - 19π/12
Evaluate the difference
Reference angle = 5π/12
Hence, the reference angle is 5π/12
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If a = 12 and 120% of a is equal to 80\% of bthen what is a + b ?
Answer:
The answer is 30
Step-by-step explanation:
First you have to find 120% of a (12).
\( \frac{12}{1} \times \frac{120}{100} = 14.4\)
Therefore; 14.4 is 80% of b, and we are trying to find 100% of b
\(14.4 = 80\% \\ x = 100\%\)
we do not know what is 100% therefore we call it *x*. In order to find this unknown value *x* we cross multiply.
\(14.4 \times 100\% = 80\% \times x\)
This is the same as saying;
\(14.4 \times 1 = x \times \frac{4}{5} \)
100% percent would be 1 because it is the whole number we are trying to find. The 80% would be 4/5. To get 4/5 you can simply break down 80/100 ( this is 80% as a fraction).
so the new equation is: 14.4= 4/5x
We divide both sides by 4/5. Then we will get x tobe equal to 18. Therefore b is 18. We were asked to find (a + b) so. 18+12 = 30
Resolución de conversión de unidades
Answer:
= 3916624286969936 \(\frac{gr ft^{2} }{hora^{3} }\)
Step-by-step explanation:
1 kg = 1000 gr
7.8kg = 7.8*1000 = 7800 gr
1m = 3.281 ft
(1m)² = (3.281ft)² = 10.765ft²
1 hora = 3600 seg
1 seg = 1/3600 = 0.0002778 horas
(1 seg)³ = (0.0002778horas)³ = 0.0000000000214335horas³
Entonces:
7.8kg m²/seg³ = 7800g * 10.765ft / 2.14335*10⁻¹¹
= 3916624286969936 (gr ft²)/hora³
= 3.916 * 10¹⁵
what are two ratios that are equivalent to 12:13?
Answer:
24:26 and 36:39 are two ratios that are equivalent to 12:13.
Step-by-step explanation:
A rod is sliding down the side of a wall such that the height is decreasing at a rate of 5 inches per second. If the rod is 174 inches long, what is the rate of change of the distance between the bottom of the rod and the base of the wall when the height is 35 inches?
Answer: The rate of change of the distance between the bottom of the rod and the base of the wall when the height is 35 inches = 1.02675 inches per second.
Step-by-step explanation:
Let h = height, x= distance between the bottom of the rod and the base of the wall.
Given: \(\dfrac{dh}{dt}\) = 5 inches per second
Consider the diagram (given in the attachment below):
By Pythagoras theorem, we have
\((174)^2=h^2+x^2\ \ (i)\\\\$$30276=35^2+x^2 \ \ \ [h=35 \ in.]\\\\ 30276=35^2+x^2 \\\\ 30276=1225+x^2\\\\ x^2=30276-1225\\\\ x^2 = 29051 \\\\ x=\sqrt{29051}\approx170.447 in.\)
Differentiate both sides of (i) w.r.t t, we get
\(0=2x\dfrac{dx}{dt}+2h\dfrac{dh}{dt}\\\\\dfrac{dx}{dt}=\dfrac{-h}{x}\dfrac{dh}{dt}\)
\(\dfrac{dx}{dt}=\dfrac{-35}{170.44}(-5)=1.02675\text{ inches per second }\)
Hence, the rate of change of the distance between the bottom of the rod and the base of the wall when the height is 35 inches = 1.02675 inches per second.
I will give brainliest and ratings if you get this correct
A. The firm's short-run total cost curve can be calculated as TC = 2K + 4L. The short-run average cost curve function will be SAC = TC/Q, where Q is the output.
B. The firm's short-run marginal cost function is MC = 4/Q. The short-run total cost (STC) at 25 and 200 levels of output will be 800 and 2400 respectively. The short-run average cost (SAC) at 25 and 200 levels of output will be 32 and 12 respectively. The short-run marginal cost (SMC) at 25 and 200 levels of output will be 16 and 8 respectively.
C. The graph of the SAC and SMC curves is shown below.
SAC and SMC Graph
D. The SMC curve intersects the SAC curve at its lowest or minimum point because at this point, the SAC curve is at its most cost-efficient level, meaning that the firm's costs are minimized. This is because at this point, the marginal cost is lower than the average cost, meaning that the firm can produce additional units of output with a decreasing cost.
I don't know how to do.
Factor the algebraic expression below in terms of a single trigonometric function.
Let a = sin x.
Hence, the expression will become:
\(a^2+a-2\)Then, let's factor out the expression above. Here are the steps:
1. Find factors of the constant term -2 that will result in the middle term which is 1.
Factors of -2 are:
a. 1 and -2 → sum is -1
b. -1 and 2 → sum is 1
Hence, the factors of -2 that will result in 1 are -1 and 2.
2. Applying the factors -1 and 2, the factors of the expression are:
\((a-1)(a+2)\)Since we let a = sin x, replace "a" in the factors above with sin x.
The factors of the given algebraic expression are [sin (x) - 1][sin (x) + 2].
\([sin(x)-1][sin(x)+2]\)Katherine and Adam need a rug for their living room. They have purchased a rectangular rug that has a width of 5��2+ 3�� ft. and a length of 4 ��2+ 2 ft
In the space below, draw a sketch of the rug.
What is the perimeter of the rug?
Their friend, Lewis, has written the expression shown in the box below to represent the perimeter of the rug.
9��2+ 5��2
Is Lewis correct or incorrect?
Lewis also predicts that an expression representing the area of the rug will be a binomial.
Is Lewis correct or incorrect?
Answer; put the question again l cant see it
Step-by-step explanation:
What is the perimeter of a rectangle with a base of 9 ft and a height of 10 ft?
Answer: The perimeter of a rectangle is found by adding up all four sides. For this rectangle with a base of 9 ft and a height of 10 ft, the two base sides have a length of 9 ft each, and the two height sides have a length of 10 ft each. Therefore, the perimeter is:
P = 2(9 ft) + 2(10 ft) = 18 ft + 20 ft = 38 ft
So the perimeter of the rectangle is 38 feet.
Step-by-step explanation:
i giveee brainlilstttttttt
Answer:
A
Step-by-step explanation:
Answer:
thanksssssssss
Step-by-step explanation:
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What is the 20% of 40% of 1250?
can you let me know how pls
Step-by-step explanation:
First, 40 percent of 1250 = 750
20 percent of 750 = 600
I don't know if this is correct I just did what my mind said sooo
Line a is parallel to line b. If the
measure of Z2 is 78°, what is the
measure of Z5?
78=21
34
6.5
718
Enter
Answer:
102
Step-by-step explanation:
Find the volume of the composite. The solid below is a square prism with a cylinder
cut out of it. Round to the nearest whole centimeter.
Answer:
17,242 cm³
Step-by-step explanation:
Step 1:
Volume of square prism = (area of base) * height
Volume of square prism = (25 * 30) * 25
Volume of square prism = 750 * 25
Volume of square prism = 18,750 cm³
Step 2:
Volume of cylinder = (area of base) * height
Volume of cylinder = (π * (8/2)²) * 30
Volume of cylinder = 16π * 30
Volume of cylinder = 480π
Volume of cylinder ≈ 1,508 cm³
Step 3:
Volume of composite = (Volume of square prism) − (Volume of cylinder)
Volume of composite = 18,750 cm³ − 1,508 cm³
Volume of composite = 17,242 cm³
What is the slope of a line that is parallel to the line y = 3/4x + 2?
Answer:
E
Step-by-step explanation:
1+2+2+1
Please answer !!!!
25 points
Answer:acd
Step-by-step explanation:yw