Four sizes of scaled text are shown. What is the unknown scale size?
Answer:
font size of top line will be 1.067
Step-by-step explanation:
Scale factor between 4th line text size to the 3rd line text will be
= [tex]\frac{0.937}{0.878}=1.067[/tex]
Scale factor between 3rd line and second line will be = [tex]\frac{1}{0.937}=1.067[/tex]
Therefore, scale factor between 2nd and 1st text size will be = [tex]\frac{x}{1}=1.067[/tex]
x = 1.067
It reveals that the font size of top line will be 1.067
find the surface area of a triangular prism that is 16 inches long 12 inches wide and 5 inches high
A. 714in2
B. 644 in2
C. 960 in2
D. 689 in2
Factor the expression. 40z – 20
a) 2z - 1
b) 2(20z-10)
c) 20(2z-1)
d) 20(2Z-20)
Answer:
[tex]\bf\pink{20(2z-1)}[/tex]Step-by-step explanation:
Given Expression :-[tex]\rm\gray{40z-20}[/tex]Steps to factorise :-[tex]\\\to\:\:\to\:\:\rm\red{40z - 20}[/tex]
Factor out [tex]\bf\blue{20}[/tex] from the expression[tex]\\\to\:\:\to\:\:\rm\green{20(2z-1)} \\ [/tex]
(Refer the attachment for graph representation)
Graph Details :-[tex]\bigstar\:\:\bf\purple{y = 40z-20} \\ [/tex]
[tex]\rm{Root \: \bigg( \dfrac{1}{2}, \:0\bigg) }[/tex][tex]\rm{ Domain \: \:z \: \in\:{\mathbb{R}}}[/tex][tex]\rm{Range \: \:y \: \in\:{\mathbb{R}}}[/tex][tex]\rm{Vertical \: intercept\:\:(0,\:-20)}[/tex]The results of a survey are shown below.in the survey,12 students said that they would like to learn French.
hey can you please help me posted picture of question
What is the square root 25 multiplied by 40 divided by 2
Lena made 32 ounces of a fruit drink mix using pineapple juice and grapefruit juice. The number of ounces of pineapple juice in the fruit drink mix is 5 more than 2 times the number of ounces of grapefruit juice in the fruit drink mix. Which graph shows the number of ounces of pineapple juice, x, and the number of ounces of grapefruit juice, y, in the fruit drink mix?
Landry is opening two savings accounts. He is opening the first account with an initial deposit of $500. The account will compound continuously each year at a rate of 3%.
He is opening the second account with an initial deposit of $300. The account will compound continuously each year at a rate of 5%.
Landry would like to know how long it will take for the balance of the two accounts to be equal.
Create a system of equations to model the situation above, and use it to determine if there are any solutions. If there are any solutions, determine if they are viable or not.
There are two solutions and both are viable.
There is only one solution and it is viable.
There is only one solution and it is not viable.
There are no solutions.
Answer:
B. there is only one solution, and it is viable
Step-by-step explanation:
Use common sense to determine whether the given event is impossible; possible, but very unlikely; or possible and likely.
An accountant was struck by lightening three times in his lifetime.
Possible and likely
Possible, but very unlikely
Impossible
Option B is the right answer.
Step-by-step explanation:
An accountant was struck by lightening three times in his lifetime. This event is Possible, but very unlikely.
We know that a probability near 0 means an unlikely event. Probability around 1/2 indicates an event that is neither unlikely nor likely. Similarly, probability near 1 indicates a likely event.
Here, in a lifetime the accountant was struck 3 times. If the average lifetime is 70 years, so probability becomes [tex]\frac{3}{70}= 0.04[/tex]. This is close to zero, indicating that the event is very unlikely.
And people are struck by lightening so it is a possible event.
Combining both, we get option B as the final answer.
Which equation could have been used to create this function table? 1 2,3 6,4 8,5 10, 10 20 A. y = 5x B. y = x + 1 C. y = x + 2 D. y = 2x
The correct equation used to create the function table provided is Option D: y = 2x, which indicates a linear relationship where y is twice the value of x.
The function table given in the question indicates the relationship between values of x and their corresponding y values. To determine which equation was used to create this table, you can compare the differences between these values. In the given pairs (1, 2), (3, 6), (4, 8), (5, 10), and (10, 20), it is observed that the y values are exactly twice the x values. Therefore, the equation representing this relationship must be y = 2x, which is a linear function with a slope of 2.
Looking at the options provided, Option D: y = 2x is the correct one, as it fits the pattern shown in the function table: for every unit increase in x, y increases by 2 units, implying a line with a slope of 2.
Past experience indicates that the time re- quired for high school seniors to complete a standard- ized test is a normal random variable with a standard deviation of 6 minutes. test the hypothesis that σ = 6 against the alternative that σ < 6 if a random sample of the test times of 20 high school seniors has a standard deviation s = 4.51. use a 0.05 level of significance.
At 0.05 level of significance, there is sufficient evidence to support the alternative hypothesis that [tex]\sigma[/tex] < 6.
To test the hypothesis that the standard deviation ([tex]\sigma = 6[/tex] ) against the alternative that ( [tex]\sigma = 6[/tex] ), we can use a chi-square test.
The test statistic for a chi-square test is given by ( [tex]\chi^2 = \frac{(n-1)s2}{\sigma2}[/tex]), where:
The sample size = [tex]n[/tex]
The sample standard deviation = [tex]s[/tex]
The hypothesized standard deviation = [tex]\sigma[/tex]
The sample size, n = 20
The sample standard deviation, s = 4.51
The hypothesized standard deviation, [tex]\sigma[/tex] = 6
Substituting these values into the formula:
[tex][ \chi^2 = \frac{(20-1)(4.51)2}{62} \approx 14.13 ][/tex]
The degrees of freedom for the test is ( n - 1 = 20 - 1 = 19 ).
The test statistic for our chi-square test is ([tex][ \chi^2 = \frac{(20-1)(4.51)2}{62} \approx 14.13 ][/tex] ).
The critical value for a chi-square distribution with 19 degrees of freedom at the 0.05 level of significance is approximately 30.14.
Since our test statistic ([tex]\chi^2 = 14.13[/tex] ) is less than the critical value (30.14), we reject the null hypothesis that [tex]\sigma[/tex] = 6 at the 0.05 level of significance.
Thus, we have sufficient evidence to support the alternative hypothesis that [tex]\sigma[/tex] < 6, suggesting that the standard deviation of the time required for high school seniors to complete the standardized test is less than 6 minutes.
Mrs. Wilton is planning a rectangular flower box for her front window. She wants the flower box to hold exactly 16 cubic feet of soil. How many different flower boxes, all with the whole-number dimensions and a different-size base, will hold exactly 16 cubic feet of soil.
There are 3 different sizes of flower boxes that have different dimensions. Then the dimensions will be 2 by 1, 2by 3, and 2 by 4.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Mrs. Wilton is planning a rectangular flower box for her front window.
She wants the flower box to hold exactly 16 cubic feet of soil.
Let the height of the flower boxes will be 1 foot.
Then the number of the flower boxes with the whole dimensions and different-size base will be
Volume = Area × 1
Area = 16 square ft.
There are 3 different sizes of flower boxes that have different dimensions. Then the dimensions will be
Area = 16
Area = 2 + 6 + 8
Area = 2 × 1 + 3 × 2 + 2 × 4
Then the dimensions are 2 by 1, 2by 3, and 2 by 4.
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If it takes 2 nurses 2 minutes to measure the blood pressure of 2 patients, how long would it take 200 nurses to measure the blood pressure of 200 patients (in minutes)?
Answer:
it will take 2 minutes for 200 nurses to measure the blood pressure of 200 patients .
Step-by-step explanation:
We know that the work-time and number of labor and efficiency formula is given by:
[tex]Efficiency=\dfrac{Number\ of\ labor\times Time}{Work\ done}[/tex]formula is given by:
Here Number of labor=Number of nurses.
Work=Number of patients whose blood pressure were noted.
As the efficiency will be same this means that:
[tex]\dfrac{2\times 2}{2}=\dfrac{200\times x}{200}[/tex]
where x denotes the number of time taken by 200 nurses.
Hence,
[tex]x=2[/tex]
Hence, the answer is:
2 minutes.
The Pyramid of Giza is one of the largest pyramid structures still standing in Egypt. It is a right pyramid with a square base, a base length of 230 m, and height of 150 m. The base is ___ m2. The volume is ___ m3.
The base area of the pyramid is 52900 m².
The volume of the pyramid is 2645000 m³.
Volume of a square based pyramidv = 1 / 3 B h
where
B = base area
h = height
Therefore,
Base area = 230 × 230
Base area = 52900 m²
h = 150m
B = 52900 m²
Therefore,
V = 1 / 3 × 52900 × 150
V = 7935000 / 3
V = 2645000 m³
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the weight of an object on mars varies directly with its weight on earth. an object that weighs 50 pounds on mars weighs 150 pounds on earth. if an object weighs 120 pounds on earth, write and solve a direct variation equation to find how much an object would weigh on mars.
To find the weight of an object on Mars, we can use a direct variation equation. By finding the constant ratio from the given values, we can then solve for the weight on Mars when the weight on Earth is known. In this case, the object would weigh 40 pounds on Mars if it weighs 120 pounds on Earth.
Explanation:To solve this problem, we will use the concept of direct variation. The weight of an object on Mars varies directly with its weight on Earth. This means that the weight on Mars can be found by multiplying the weight on Earth by a constant ratio. Let's represent the weight on Mars as WM and the weight on Earth as WE. According to the problem, an object that weighs 50 pounds on Mars weighs 150 pounds on Earth. This gives us the following direct variation equation:
WM = k * WE
where k is the constant ratio.
We can now substitute the given values: 50 pounds for WM and 150 pounds for WE.
50 = k * 150
To solve for k, divide both sides of the equation by 150:
k = 50 / 150
k = 1 / 3
Now that we have the value of the constant ratio, we can find the weight of an object on Mars when it weighs 120 pounds on Earth. Let's represent the weight on Mars as x and the weight on Earth as 120:
x = (1 / 3) * 120
x = 40
Therefore, the object would weigh 40 pounds on Mars.
If point (4,5) is in the graph of a function, which equation must be true?
Answer:
Step-by-step explanation:
C) f(4)=5
Graph the inequality y<|x+2|. Which point is not part of the solution?
A) -1,-2
B) 1,2
C) 0,0
D) -1,2
Answer:
D) (-1, 2)
Step-by-step explanation:
See the graph below. The indicated point is not in the shaded region, hence not part of the solution.
From a basket of mangoes, the king took 1/6, the queen took 1/5 of the remainder, the three chief princes to ¼, 1/3, and ½ of the successive remainders, respectively. the youngest child took the remaining 3 mangoes. how many mangoes were in the basket originally
Final answer:
The original basket contained 72 mangoes, determined by working backward from the known remainder of 3 after the sequential distribution between the king, queen, and princes.
Explanation:
From a basket of mangoes, the distribution among the royal family leads to a classic fractional subtraction problem. The solution involves working backward from the known remainder. The youngest child took the remaining 3 mangoes, which indicates that this was what was left after the king, the queen, and the three chief princes took their respective shares.
Let's denote the original number of mangoes as x. The king took 1/6 of x, leaving 5/6x. The queen then took 1/5 of the remainder (5/6x), leaving 4/5 * 5/6x = 4/6x or 2/3x. Successively, the three chief princes took 1/4, 1/3, and 1/2 of their respective remainders, each action further reducing the quantity of mangoes. The problem states that after these distributions, 3 mangoes were left, which were taken by the youngest child.
To find the original number of mangoes, we begin by denoting the final 3 mangoes as the remaining half after the last prince's share, work through the inverse operations for each prior transaction, and solve for x. Through this back calculation, we find that the original number of mangoes was 72.
Cameron used 1 3/4 ounces of hydrochloric acid in one experiment. She used 2 1/8 ounces of the acid in a second experiment. How much more acid did Cameron use in the second experiment?
Answer:
Amount required is [tex]x=\frac{3}{8}[/tex]
Step-by-step explanation:
Given : Cameron used [tex]1\frac{3}{4}[/tex] ounces of hydrochloric acid in one experiment. She used [tex]2\frac{1}{8}[/tex] ounces of the acid in a second experiment.
To find : How much more acid did Cameron use in the second experiment?
Solution :
In one experiment,
Cameron used [tex]1\frac{3}{4}[/tex] ounces of hydrochloric acid
i.e [tex]1\frac{3}{4}=\frac{7}{4}[/tex]
In second experiment,
She used [tex]2\frac{1}{8}[/tex] ounces of the acid.
i.e. [tex]2\frac{1}{8}=\frac{17}{8}[/tex]
Let x amount more she used then experiment 1 in experiment 2.
So, the equation became
[tex]\frac{7}{4}+x=\frac{17}{8}[/tex]
[tex]x=\frac{17}{8}-\frac{7}{4}[/tex]
[tex]x=\frac{17-14}{8}[/tex]
[tex]x=\frac{3}{8}[/tex]
Therefore, Amount required is [tex]x=\frac{3}{8}[/tex]
Find the directional derivative of f(x, y, z) = xy + yz + zx at p(1, −1, 7) in the direction from p to q(2, 4, 5). duf(1, −1, 7)
The directional derivative of f(x, y, z) = xy + yz + zx at p(1, -1, 7) towards q(2, 4, 5) is found by first calculating the unit vector in the direction from p to q, then the gradient of f at p, and calculating the dot product of the two vectors. The directional derivative comes out to be 16/ √30.
Explanation:The directional derivative of the function f(x, y, z) = xy + yz + zx at a point p(1, -1, 7) towards the point q(2, 4, 5) can be found by first getting the unit vector in the direction from p to q, then calculating the gradient of the function at p, and finally calculating the dot product of these two vectors (the unit vector and the gradient of the function).
First, calculate the unit vector u = (q - p) / |q - p|. That gives u = (1, 5, -2), and normalize it to get u = 1/ √30 (1, 5, -2).
Next, get the gradient of the function at p(1, -1, 7), which is the vector of first order derivatives. The partial derivatives of f(x, y, z) with respect to x, y, z are y+z, x+z, and x+y respectively. This gives the gradient vector at p as (-8, 8, 0).
Finally, the directional derivative is the dot product of the unit vector and the gradient, which comes out to be 1/ √30 * ((1*-8) + (5*8) + ((-2)*0)) = 16/ √30.
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what are the zeroes of 2x squared plus 6x minus 8
What is the value of 1*2+ 3 / 6*5 - 4? Express as a fraction.
When scholastic achievement test scores (sats) are sent to test-takers, the percentiles associated with scores are also given. suppose a test-taker scored at the 59th percentile on the verbal part of the test and at the 36th percentile on the quantitative part. interpret these results?
Two sides of a parallelogram measure 60 centimeters and 40 centimeters. If one angle of the parallelogram measures 132 degrees, find the length of each diagonal.
Final answer:
The lengths of the diagonals in the parallelogram can be calculated using the properties of vectors and the law of cosines with the given side lengths and angle.
Explanation:
To find the length of each diagonal in a parallelogram with sides measuring 60 centimeters and 40 centimeters and one angle of 132 degrees, we can leverage the properties of vectors and the law of cosines. It is known that one diagonal is the vector sum of the sides, while the other diagonal is the vector difference of the sides.
First, let's compute the length of the shorter diagonal, which is the vector sum of the two sides:
Shorter diagonal (Ñ) = A + B
Using the law of cosines for finding the length of a diagonal, we get:
Ѳ = 60² + 40² - 2 * 60 * 40 * cos(132°)
After computing this, we find the length of the shorter diagonal.
Next, we calculate the length of the longer diagonal, which is found by subtracting the vectors of the two sides:
Longer diagonal (D) = A - B
Again using the law of cosines:
D² = 60² + 40² - 2 * 60 * 40 * cos(48°)
After computation, we find the length of the longer diagonal.
Through these calculations using the provided formulae and the law of cosines, both diagonals' lengths can be established.
A group would like to estimate the percentage of town residents who would support a teen curfew.
Which statement describes a method that will help the group accurately estimate this percentage?
Take a random sample of towns in the state. Ask an administrator in the city office whether the town has a teen curfew, and then calculate the percentage of the total who say "yes."
Identify all nearby towns that have a teen curfew. Contact the mayor of each of those towns and ask whether he or she thinks the curfew is a good policy. Calculate the percentage of the total who say "yes."
Contact every parent who lives in the town and ask whether they support a teen curfew. Calculate the percentage of the total who say "yes."
Take a random sample of residents in the town, and ask each resident in the sample whether or not they support a teen curfew. Then calculate the percentage of the total who say "yes."
The correct statement that describes a method that will help the group accurately estimate this percentage is;
⇒ Take a random sample of residents in the town, and ask each resident in the sample whether or not they support a teen curfew. Then calculate the percentage of the total who say "yes."
What is Random Sampling?Random sampling is defined as a sampling method that utilizes randomization of sample selection.
In random sampling, each sample has the same probability of being selected as that of other samples to be selected to serve as a representation of an entire population.
Now, in this question, since the group would like to estimate the percentage of town residents who would support a teen curfew, then the sampling method they should use is random sampling which is in option C.
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Use the euclidean algorithm to find
a.gcd(12, 18).
b.gcd(111, 201).
c.gcd(1001, 1331).
d.gcd(12345, 54321).
e.gcd(1000, 5040). f ) gcd(9888, 6060).
The Euclidean Algorithm is used to find the greatest common divisor (GCD) of two numbers, this method has been applied to find the GCDs of multiple pairs of numbers.
Explanation:The Euclidean Algorithm is basically a method to find the greatest common divisor (GCD) of two numbers. It is based on the principle that the GCD of two numbers is the same as the GCD of the remainder when the larger number is divided by the smaller one.
gcd(12, 18): Using the Euclidean algorithm, 18 = 12*1 + 6. Now replace 18 with 12 and 12 with the remainder 6. So, 12 = 6*2 + 0. As we reached 0, our GCD is 6. gcd(111, 201): Apply the Euclidean algorithm, the GCD is 3. gcd(1001, 1331): The GCD is 11. gcd(12345, 54321): The GCD is 3. gcd(1000, 5040): The GCD is 40. gcd(9888, 6060): The GCD is 68. Learn more about Euclidean Algorithm here:
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Meg needs to have her car repaired. Parts will cost $905, and the labor cost for the job is $499. What will be the total cost for the job? Check your answer using the inverse operation
Based in the graph, what is the initial value of the linear relationship
A)-4
B)-3
C)5/3
D)5
Answer:
D)5
Step-by-step explanation:
The initial value of the linear relationship is the value that exists in the "Y" axis when the "x" value is 0, as you can see in the graph, when the X value is 0, the Y value is 5, so the inital value of the linear relationship is 5.
If you wish to calculate this on an inequality, you just have to insert in the inequality 0 as the value for x, and you will get as a result the initial value.
What is the following sum? 4(5 sqrt x^2y)+3(5 sqrt x^2y)
Answer:
7(5 sqrt x^2y) or C
Step-by-step explanation:
A salesperson has to drive 500 miles. For the first three hours she drove at 65 mi/h. For the next two hours she drove at 55 miles per hour. How many more miles does she have to drive?