y is directly proportional to x. When x = 2, y = 64. Find x when y = 80​

The sum of two number is 92. Their difference i 20Let x and y represent the 2 number. Let x=the lager value and smaller valuex = 92 + 20 = 11,y = 92 - 20 = 72

Let x = the larger value and y = the smaller value.

We know that the sum of x and y is 92, so

x + y = 92

We also know that the difference between x and y is 20, so

x - y = 20

Add the two equations to get

2x = 112

Divide by 2 to get

x = 112

Substitute x = 112 into the first equation to get

112 + y = 92

Subtract 112 from both sides to get

y = 72

Therefore, the two numbers are x = 112 and y = 72.

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In the first circle, the measure of angle ABC is 24°

In the second circle, the measure of angle ABC is 20°

From the question, we are to determine the measure of angle ABC

In the first diagram,

The measure of the arc is 48°

From one of the circle theorems, we have that

The angle subtended by an arc in a circle is twice the angle subtended at the circumference.

Then, we can write that

2 × ∠ ABC = 48°

∠ ABC = 48°/2

∠ ABC = 24°

Question 5

Using the same theorem,

The angle subtended by an arc at the center of the circle is twice the angle subtended at the circle

∠ ABC = 1/2 × 40°

∠ ABC = 20°
Hence, the measure of the angle is 20°

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Distance covered by Yochanan by walking = 5 km

Distance covered by Yochanan by bus = 30 km

Given the values in the question,

The average speed of Yochanan when he walked to the bus stop from home = 5 km/h

The average speed of the bus till Yochanan reached his school = was 60 km/h

The total distance between his school from home = is 35 km

Time is taken by the entire trip = 1.5 hours

Relation between Distance, Time, and speed,

⇒ Average Speed = [tex]\frac{Distance}{Time}[/tex]

Let us consider that Yochanan walked = a km

The bus travelled = 35 - a

We know that the total time is constant so,

⇒ T = T1 + T2

⇒ 1.5 = [tex]\frac{x}{5} + \frac{35-a}{60}[/tex]

Solving for a,

⇒ 1.5 = [tex]\frac{12a + 35 - a}{60}[/tex]

⇒ 11 a + 35 = 90

⇒ 11 a + 55

⇒ a = 5

The distance covered by Yochanan by walking = a = 5 km

Distance covered by bus = 35 - a

= 35 - 5

= 30 km

Therefore, the distance covered by Yochanan by walking = is 5 km, distance covered by Yochanan by bus = is 30 km

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Yochanan walked from home to the bus stop at an average speed of 5 km/h he immediately got on his school bus and traveled at an average speed of 60 km/h until he got to school. the total distance from his home to school is 35 kilometers, and the entire trip took 1.5 hours. how many kilometers did Yochanan cover by walking, and how many kilometers did he cover by traveling on the bus? Yochanan walked kilometers and traveled kilometers on the bus.

Answer:

Step-by-step explanation:

To find the value of z such that 0.12 of the area lies to the right of z, we need to know the distribution of the data and the total area under the curve. If the data follows a normal distribution, the area under the curve is always 1, and 0.12 of the area corresponds to a z-value of approximately 0.84.

We can use a standard normal table or a calculator to find the exact value of z. For example, using a standard normal table, we can find that the z-value corresponding to an area of 0.12 to the right of z is 0.8416.

Therefore, the value of z such that 0.12 of the area lies to the right of z is approximately 0.84.

The slope of the roof is 0.25

What is a slope ?

A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. No matter which two locations on the line you choose, the slope of a line is always constant (it never varies).

The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. And b is the value of b at the y-intercept (0, b).

To find slope

= 6.25 / 25

= 0.25

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Answer: 6000 students

Step-by-step explanation:

First, we find the 40% that the university accept

40% = 0.4

Take 30000 times 0.4 = 12000 students got accept

Now we find the 50%

50% = 0.5

Take 12000 times 0.5 = 6000 students

6000 students would actually enroll

Answer:

b) arithmetic

Step-by-step explanation:

Knowledge Needed

c and d are not valid sequence types.

Geometric Sequences are when the values of terms are found by multiplying the previous term's value by the same number.

Example:

1, 2, 4, 8, 16

x2

2, 6, 18, 54, 162

x3

20, 10, 5, 2.5, 1.25

x0.5

Arithmetic Sequences are when the values of terms are found by adding the previous term's value by the same number.

Example:

5, 6, 7, 8

+1

7, 19, 31, 43

+12

9, 6, 3, 0

-3

Question

Examine the sequence. From viewing the first 2 terms, we know that it can either be a geometric sequence that multiplies by 11/3 every time the term increases or an arithmetic sequence that adds 8 every time the term increases.

Looking at the 2nd and 3rd term, we know it is an arithmetic sequence because 19 is not equal to 11 times 11/3.

The price of the watch before the discount is calculated to be £24.44.

As the total price of the watch and a pair of trainers is £53. 55 and the price of the trainer before the discount was £38, we first calculate the price of the trainers after the discount as follows;

discount on a pair of trainers = 15/100 × 38 =  £5.7

cost of trainers after discount =  £38 - 5.7 =  £32.3

Now the price of the watch after the discount can be calculated by subtraction as follows;

price of watch after discount = total price - price of trainers after discount

price of watch after discount =  £53. 55 - £32.3

price of watch after discount = £21.25

Now the price of the watch before the discount can be calculated as follows;

price of watch before discount = £21.25 × 15/100

price of watch before discount = £21.25 + £3.1875

price of watch before discount = £24.44

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The sign change of the expression ax + b = cx + d in the conditions are solved to be

a. 0 < b < d and a < c

b. d < b < 0 and a < c

The given expression is

ax + b = cx + d

comparing the conditions

a. 0 < b < d and a < c

here b is non negative number and less than d a is also less than c. hence

ax + b = cx + d

ax - cx = d - b

ax - cx will be negative

d - b will be positive

this will lead to a negative solution since positive divided by negative  give negative

b. d < b < 0 and a < c

ax + b = cx + d

ax - cx = d - b

d - b = negative

ax - cx = negative

negative dividing negative is positive hence a positive solution

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Answer:

A. Alternate exterior angles

Step-by-step explanation:

Alternate exterior angles are congruent angles that are outside the parallel lines. That is why their name is alternate exterior angles since they are exterior from parallel lines.

The value of x is in the solution set of the inequality 9(2x + 1) < 9x – 18 is -4.

Inequality is defined as relationship between non-equal numbers or expressions. The solution set of an inequality is the set of values that satisfies the given inequality.

To determine the solution set of the given inequality, isolate the variable to one side and simplify.

9(2x + 1) < 9x - 18

18x + 9 < 9x - 18

18x - 9x < -18 - 9

9x < -27

x < -3

x = (-∞, -3)

Hence, the solution set of the given inequality is the set of numbers less than -3. Among the given choices, only -4 is less than -3. Therefore, the value of x is -4.

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Answer: -4

Step-by-step explanation: edge2020

Let's say Chloe spent X

Then Amy spent 60% more so Amy spent

X+60% of X =X + 0.6X =1.6X

Becky spent 15% of what Chloe spent so amount spent by Becky =15% of X = .15X

Now, in total, they spent 0.15X+ X + 1.6X =2.75X which is given as £55

So , X=55/2.75 = 20

Amount spent by Amy = 1.6X = 1.6 *20 =£32

It will take 35 years to double the population

Percentages are just fractions with a denominator of 100. To show that a number is a percentage, we place the percent sign (%) next to it. For instance, if you properly answered 68 out of 100 questions on a test, you would have received a 68% grade (68/100).

According to the given information

Let [tex]P(0)[/tex] be initial population

and K be the growth rate

Then Population of the country after t years

[tex]P = P(0)e^{Kt}[/tex]

Let x be the present population

2x will be the double of present population

And we know

The growth rate K = 0.02%

So

The value of t could be determined as follows

[tex]xe^{0.02t}=2x[/tex]

[tex]e^{0.02}=2[/tex]

[tex]0.02t=ln(2)[/tex]

Multiply both sides by 1000

0.02t × 1000 = ln(2) × 1000

Refine

20t = ln(2) × 1000

Divide both sides by 20

[tex]\frac{20t}{20}=\frac{ln(2).1000}{20}[/tex]

t = [tex]ln(2).500[/tex]

t = 0.693×50

t = 34.65 years

t = 35 years

It will take 35 years to double the population

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Answer:

it would be quadrant |||

so answer choice C

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]log_{10}(2000xy)-(log_{10}x})(log_{10}y)=4\\\\log_{10}(2000(xy))-log_{10}(xy)=4\\\\log_{10}(2000)+log_{10}(xy)-log_{10}(xy)=4\\\\log_{10}(2(1000)=4\\\\log_{10}2+log_{10}(1000)=4\\\\log_{10}2+log_{10}(10^3)=4\\\\log_{10}2+3log_{10}(10)=4\\\\log_{10}2\approx0.3\\\\Hence,\\\\log_{10}2+3\neq 4[/tex]

[tex]log_{10}(2yz)-(log_{10}y)(log_{10}z)=1\\\\log_{10}(2(yz))-log_{10}(yz)=1\\\\log_{10}2+log_{10}(yz)-log_{10}(yz)=1\\\\log_{10}2\neq 1[/tex]

[tex]log_{10}(zx)-(log_{10}z)(log_{10}x)=0\\\\log_{10}(zx)-log_{10}(zx)=0\\\\0\equiv0[/tex]

If a hypothesis test is significant at level α = 0.05, then the P-value is less than or equal to 0.05 or P-value ≤ 0.05.

The P-value is a measure of the strength of the evidence against the null hypothesis. It is the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. If the P-value is less than or equal to the significance level α, it means that the observed evidence is unlikely to have occurred by chance under the null hypothesis, and we can reject the null hypothesis in favor of the alternative hypothesis.

For example, if the P-value of a hypothesis test is 0.03, it means that there is a 3% chance of obtaining the observed test statistic (or a more extreme one) if the null hypothesis is true. Since this is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.

Hence, if a hypothesis test is significant at level α = 0.05, then P-value ≤ 0.05.

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According to the standard normal distribution table, the area under the curve that is 2.25 standard deviations below the mean is approximately 1.22%.

Standard deviation is a measure of the spread or dispersion of a set of data. It tells you how much the individual values in the set differ from the mean (average) of the set.

The formula for calculating the standard deviation of a set of n data points:

Standard deviation = sqrt(((x1 - mean)^2 + (x2 - mean)^2 + ... + (xn - mean)^2) / n)

First, we need to calculate the number of standard deviations that the guarantee period of 24 months is from the mean of 33 months. We can do this by subtracting the mean from the guarantee period and dividing by the standard deviation:

(24 - 33) / 4 = -9 / 4 = -2.25

Since we are assuming that the distribution of battery lifetimes is normal, we can use the standard normal distribution table to look up the area under the curve that is 2.25 standard deviations below the mean. This area represents the proportion of batteries that will have to be replaced under the guarantee.

According to the standard normal distribution table, the area under the curve that is 2.25 standard deviations below the mean is approximately 0.0122. This means that approximately 1.22% of the batteries will have to be replaced under the guarantee.

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The function has no vertical asymptotes and the horizontal asymptotes of the function is y=0.

In the given question,

Consider the following function.

f(x) = e^{−x^2}

We have to find the vertical asymptote(s), x = Find the horizontal asymptote(s) or y = .

As we know that, a vertical asymptote is a line that runs vertically and guides the graph of the function but does not actually exist on it. Due to its position at an x-value that is outside of function's domain, it is difficult for the curve to ever pass it.

The function f(x) = e^{−x^2} has no undefined points. So the function has no vertical asymptotes.

The limit of the function at x→±∞ is calculated as follows:

[tex]\lim_{x\rightarrow \pm\infty }[/tex]f(x) = [tex]\lim_{x\rightarrow \pm\infty }[/tex]e^{−x^2}

[tex]\lim_{x\rightarrow \pm\infty }[/tex]f(x) = 0

So the horizontal asymptotes of the function is y=0.

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The right question is:

Consider the following function. (If an answer does not exist, enter DNE.) f(x) = e^{−x^2}. Find the vertical asymptote(s). (Enter your answers as a comma-separated list.) x = Find the horizontal asymptote(s). (Enter your answers as a comma-separated list.)

y =

The price that is 3rd standard above the mean, if the mean is $10000  and the standard deviation is $500 is $18500.

Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

Given:

The mean, m = $17000,

The standard deviation, σ = $500

Calculate the 3rd standard deviation as shown below,

3rd standard deviation  = mean + 3 × standard deviation

3rd standard deviation = 17000 + 3 × 500

3rd standard deviation = 17000 + 1500

3rd standard deviation = $18500

Therefore, the price that is 3rd standard above the mean, if the mean is $10000  and the standard deviation is $500 is $18500.

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Answer: $0.08

Step-by-step explanation:

First, let's find last week's price

Take 35.40 divided by 12 = $2.95 per gallon

Next, find this week's price

Take 25.83 divided by 9 = $2.87 per gallon

Then take 2.95 - 2.87 = $0.08

Answer:

x = -5; y = 5

Step-by-step explanation:

  x + 5y = 20

-2x + 7y = 45

Multiply both sides of the first equation by 2 to get 2x. Write the second equation below it and add the equations. 2x and -2x add to zero eliminating the x terms.

 2x + 10y = 40

-2x +  7y = 45

-----------------------

         17y = 85

y = 85/17

y = 5

Now use substitution in the first original equation to find x.

x + 5y = 20

x + 5(5) = 20

x = -5

Answer: x = -5; y = 5

Answer: Median is 12, mode is 5, mean is 13.71

Step-by-step explanation:

Answer:

The median is 18

The mode is 5

The mean is 13

Step-by-step explanation:

The value of the Confidence interval will be 2.898

The number of standard deviations from the t-mean distribution's is equal to a t-score. The test statistic used in t-tests and regression testing is the t-score. When the data follow a t-distribution, it may also be used to represent how distant an observation is from the mean.

The t-score formula is written as follows:t=¯¯¯x−μS√n t = x ¯ − μ S n , where ¯¯¯x, is the sample mean, is the population mean, S n is the sample size, and x is the standard deviation of the sample. Square root n must be included in the formula.

using tables of t distribution we have

alpha = 1 - 0.99 = 0.01

alpha / 2 = 0.005

df = 17

critical value or value of t score is = 2.898

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The value of the t score is 2.898 for a 99% confidence interval if we take a sample of size 18.

As per the details share in the above question are as bellow,

Confidence level = 99%

Now the significance level will be 100% - Confidence level

Substitute the value in above equation we get,

Thus, Significance level = (100% - 99%)

Significance level= 1%

Significance level=1/100= 0.01

Now the Sample size (n) = 18

Further the degrees of freedom = (n - 1)

Substitute the value in above equation we get,

Degrees of freedom= (18 - 1) = 1

Where, the t score for a 99% confidence interval is given by,

t({0.01/2},17)=2.898

Now calculating the critical value from t table we get,

Critical value or value of t score is = 2.898

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The tree will be 75 feet tall when it will be fully grown.

The total tree height is the distance between the tree's base and its highest point on the ground. A yardstick provides a quick and relatively accurate way to gauge the height of a tree.

If the tree is currently 60 feet tall and is approximately 80% of its full height, we can assume that the tree will be 100% of its full height when it is fully grown. To determine the full height of the tree, we can use the proportion:

60 feet / 80% = X feet / 100%

We can then cross-multiply to solve for X:

X = (60 feet * 100%) / 80%

= 75 feet

So, when the tree is fully grown, it will be approximately 75 feet tall.

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The present age of Jiya whose mother 12 year more than twice her age., is sixteen years and her mother present age is fourty-four years.

We have, Jiya's mother is 12 year more than twice of her age. Let "x years" and "y years" be the present age of Jiya and her mother respectively.

According to problem, 12 + 2x = y --(1)

After 8 years, her mother age = 20 years less then three times of her age.

After 8 years, age of Jiya = (x+8) years.

i.e y + 8 = 3( x+8) - 20 --(2)

we have to calculate the present ages of both. Simplify the equation (2),

y + 8 = 3x + 24 - 20

=> y + 8 = 3x + 4 => y = 3x -4 --(3)

eqution (1) and (3) represent the linear equations so, we solve these linear equations by substitution,

plugging the value of y from( 1) to (3),

12 + 2x = 3x -4

=> 3x - 2x = 12+4

=> x = 16 then y = 12 + 2×16 = 44

Hence, Jiya's age is 16 years and her mother is about 44 years.

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Answer:

65 mph;  35 mph

Step-by-step explanation:

let x = rate of car 1

x-30 = rate of car 2

distance = rate x time

6x = 600 - 6(x-30)

6x = 600 - 6x + 180

6x = 780 - 6x

12x = 780

x = 780/12 = 65 mph

x - 30 = 65 - 30 = 35 mph

Yes, this statement is correct because in quadrilaterals if two lines are parallel, then the other two sides have to be equal in length.

Triangles that are equal in all ways and interchangeable are typically described as being congruent.

A triangle with equal legs, such as an isosceles triangle, may have equal legs that are also equal to the two equal legs of another triangle with equal legs, but if the included angle is different, the triangles are not congruent.

Two sides are simply equal if their lengths are the same.

When it comes to parallelograms, both opposite side pairs are equal and parallel.

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Evelyn basis is the adjusted market value of the property and the basis would have been to Evelyn as profit

We should know that adjusted basis is the value of a property after deducting all expenses and taxes from the property.

The Adjusted basis of the property was $12,000

It was given to Sharon at fair value of $80,000

After  death of Sharon, the property was worth $85,000

Based on these figures, the basis is a gain of $(85000-80000) to to Evelyn

In conclusion, Evelyn has gained the sum of $(85000-12000)=$73000

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The solution to the system of linear equations 3y = x + 21 and y + 2/3x = 10

is (x, y) = (3, 8)

A system of linear equations is a collection of at least two linear equations.

From the question, we have the following parameters that can be used in our computation:

In this case, the system of equations is given as

3y = x + 21

y + 2/3x = 10

Next, we plot the graph of the system of equations

In this case, the point of intersection of the equations represent the solution to the system

From the graph, the lines intersect at (3, 8)

Hence, the solution is (3, 8)

In (a), we have

The lines intersect at (3, 8)

This means that

(x, y) = (3, 8)

So, we have

3 * 8 = 3 + 21 = 24

y + 2/3 * 3 = 10

The above equations are true

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