Use the Pythagorean Theorem to find the lengths of the
sides of the triangle.
26
2x-14

Answer: the slower bus travels at 55 miles per hour and the faster bus travels at 73 miles per hour.

Step-by-step explanation:

distance = rate x time

768 = 6x + 6(x + 18)

Simplifying this equation, we can distribute the 6 on the right-hand side:

768 = 6x + 6x + 108

Combining like terms, we get:

768 = 12x + 108

Subtracting 108 from both sides:

660 = 12x

Dividing both sides by 12:

x = 55

So the slower bus is traveling at 55 miles per hour. To find the speed of the faster bus, we can add 18:

x + 18 = 55 + 18 = 73

Answer: one is 55 and the other is 73

Step-by-step explanation:

lets say x is for the slower bus. for every hour the become x+x+18

and this is happening for 6 hours so its is 6(2x+18)=768

x=55

x+18=73

Step-by-step explanation:

To simplify the expression -6(4v - x - 5), we distribute the -6 to each term inside the parentheses:

-6(4v - x - 5) = -6(4v) - (-6x) - (-6)(5)

Simplifying each term:

-6(4v) = -24v

-(-6x) = 6x

-(-6)(5) = 30

Therefore,

-6(4v - x - 5) = -24v + 6x - 30

So the simplified expression is -24v + 6x - 30.

Because BF and CE bisect each other at point D, we know that angles BDC and EDC are congruent, and angles BDF and CDE are also congruent, as they are vertical angles.

In mathematics, an angle is a geometric figure formed by two rays or line segments that share a common endpoint called the vertex. The rays or line segments are called the sides of the angle.

Angles are typically measured in degrees or radians, and they are denoted using the symbol ∠. The measure of an angle is the amount of rotation needed to bring one side of the angle into coincidence with the other. A full rotation is 360 degrees or 2π radians.

Angles can be classified into different types based on their measures and their relationships with other angles. Some common types of angles include:

Acute Angle: An angle whose measure is less than 90 degrees.

Right Angle: An angle whose measure is exactly 90 degrees.

Obtuse Angle: An angle whose measure is greater than 90 degrees but less than 180 degrees.

Because BF and CE bisect each other at point D, we know that angles BDC and EDC are congruent, and angles BDF and CDE are also congruent, as they are vertical angles.

By definition of angle bisectors, we know that CD=DE and BD=DF.

Thus, the triangle congruence principle SAS (side-angle-side) allows us to deduce that Triangle BCD is congruent to Triangle ECD, since they share side CD, angle BDC and angle EDC.

Therefore, BC=CE (corresponding sides of congruent triangles are equal) and CE=EF (because CE bisects segment BF).

Thus, BC=EF, and we have proven that BC is equal to EF

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The amount of money in the account after 17 years is approximately $49,222.26.

Investment is the act of allocating resources, such as money or time, with the expectation of generating a return or profit in the future. Investment can take many forms, such as investing in stocks, bonds, real estate, or businesses.

Investment is an important tool for individuals and businesses to build wealth and achieve financial goals. By investing in assets that appreciate in value or generate income, investors can increase their net worth and achieve long-term financial stability.

When making investment decisions, investors typically consider factors such as risk, return, liquidity, and diversification. Risk refers to the possibility of losing money, while return refers to the potential profit or income generated by the investment. Liquidity refers to how easily an investment can be converted into cash, while diversification refers to spreading investment across multiple assets to reduce risk.

Using the formula [tex]V= Pe^{rt}[/tex], where P = $34300, r = 0.02, and t = 17, we can find the value of the account after 17 years:

V = 34300 * [tex]e^{0.02*177[/tex]

V ≈ $49,222.26

Therefore, the amount of money in the account after 17 years is approximately $49,222.26.

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Answer:

last 2 are b

and c

Step-by-step explanation:

Answer:

Step-by-step explanation:

Formula: A=πr2

3.14 x 17^2 = 907.46 in2

Answer:

2,500,000

Step-by-step explanation:

To write 2.5 million, you can write it as 2,500,000. This is because one million is equal to 1,000,000. So, 2.5 million is equal to 2,500,000.

Answer:

2500000 <--- in numbers

Two million and five hundred thousand OR Two and a half million

Answer:

Step-by-step explanation:

The perimeter is the distance around the edge of the shape.

    [tex]P=2+4+2+1+4+5=18cm[/tex]

Answer:

20000

Step-by-step explanation:

because the x =1 and X=2 so is 1x2=2

Apprοximately 31 mοving bοxes οn the flοοr οf the stοrage unit, given the dimensiοns οf the bοxes and the aisle.

In mathematics and geοmetry, dimensiοns refer tο the number οf cοοrdinates needed tο specify the lοcatiοn οf a pοint οr οbject in space.

Tο calculate the number οf mοving bοxes that can fit οn the flοοr οf the stοrage unit, we need tο first calculate the usable flοοr space by subtracting the width οf the aisle frοm the tοtal width οf the stοrage unit.

The usable floor space can be calculated as follows:

Usable floor space = 10 ft - 3 ft (aisle) = 7 ft

Next, we need to calculate how many boxes can fit in a row along the length and width of the usable floor space.

Along the length of the floor space, we can fit:

Number of boxes along length = 10 ft / 18 in = 20/3 boxes

Similarly, along the width of the floor space, we can fit:

Number of boxes along width = 7 ft / 18 in = 14/3 boxes

Since we can only stack the boxes one layer high, the total number of boxes that can fit on the floor of the storage unit can be calculated by multiplying the number of boxes along the length by the number of boxes along the width:

Total number of boxes = (20/3) x (14/3) = 280/9 ≈ 31

Therefore, we can fit approximately 31 moving boxes on the floor of the storage unit, given the dimensions of the boxes and the aisle.

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Answer:

14.3cm

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]a^{2}[/tex] + [tex]7^{2}[/tex] = [tex]10^{2}[/tex]

[tex]a^{2}[/tex] + 49 = 100  Subtract 49 from both sides

[tex]a^{2}[/tex] + 49 - 49 = 100 - 49

[tex]a^{2}[/tex] = 51

[tex]\sqrt{a^{2} }[/tex] = [tex]\sqrt{51}[/tex]

a = 7.14142842854  This is a rounded number.  This is an irrational number.  That means that it never repeats or terminates.  It is like [tex]\pi[/tex].

We just found the left side of the base of the triangle.  We need to double this to find FG.

7.14142842854 x 2 = 14.2828568571

Round this to 1 decimal place 14.3

Helping in the name of Jesus.

Answer: 14.28 cm

Step-by-step explanation:

So, 10 squared = 7 squared + X squared.

This can be simplified to: 100 = 49 + X squared.

Then, you subtract 49, and are left with 51 = X squared

Then, take the square root if 51, you get approx. 7.14 cm.
since this is an equilateral triangle, the answer will be the same for the second half of the base.
So, 7.14 x 2, 14.28 cm

There are 36 outcomes in Ec.

What is outcome?
An outcome is a potential outcome of an experiment or trial in probability theory.

The event E represents the sum of two rolled dice being less than or equal to 3. There are only two possible ways to get a sum of 3 or less when rolling two dice: getting a sum of 2 or getting a sum of 3.

If two dice are rolled then sample space is given by,

S = {(1,1), (1,2), (1,3), (1, 4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3, 5), (3,6)

(4,1), (4,2), (4,3), (4, 4) (4,5) (4,6),

(5,1), (5,2), (5,3), (5, 4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,3), (6,6)

n(s) = 36

Event that,

E: sum of two rolled dice is less than 3

[tex]\rm E_c[/tex]= {(1,1)}

n([tex]\rm E_c[/tex]) = 1

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Answer:

$ 922.25

Step-by-step explanation:

General equation for simple interest ... B(t)=B(0)[1+rt]B

(0)= inital amount r= simple annual interest rate t= number of yearsFor this problem,

B (2)=$850[0.0425×2}=850×1.085 =$922.25

Finding the limit of the function limx→0 ((sin( 1- cos4x))/(1 - cos4x)) = 1

The limit of a function is the value which the function tends to as the dependent variable tends to a particular value.

Since we require the limit limx→0 ((sin(1-cos4x))/(1-cos4x))

So, substituting x = 0 into the equation, we have

limx→0 ((sin(1-cos4x))/(1-cos4x)) = ((sin(1-cos4(0)))/(1-cos4(0)))

=  ((sin(1 - cos(0)))/(1 - cos(0)))

=  ((sin(1 - 1))/(1 - 1))

= sin0/0

= 0/0

Since we have an indeterminate form, we use L'hopital's rule which states that if limx→0 f(x) = limx→0 g(x) = 0,

Then limx→0 f(x)/g(x) = limx→0 f'(x)/g'(x)

So, limx→0 ((sin( 1- cos4x))/(1 - cos4x)) = limx→0 d((sin(1-cos4x))/dx/d(1-cos4x))/dx

Let 1 - cos4x = u and 4x = v

1 - cosv = u

=  limx→0 d((sin(1 - cos4x))/dx/d(1 - cos4x))/dx

=  limx→0 d((sinu)/dx/du/dx

=  limx→0 d((sinu)/du × du/dv × dv/dx ×/du/dv × dv/dx

Now du/dv = sinv and dv/dx = 4 and d

So,

limx→0 d((sinu)/du × du/dv × dv/dx ×/du/dv × dv/dx =  limx→0 d((sinu)/du × sinv × 4 ×/sinv × 4

=  limx→0 cosu × sinv × 4 ×/sinv × 4

=  limx→0 cos(1 - cos4x) × sin4x × 4 ×/sin4x × 4

= cos(1 - cos4(0)) × sin4(0) × 4 /sin(4(0) × 4

= cos(1 - cos0) × sin(0) × 4 /sin(0) × 4

= cos(1 - 1) × 0 × 4 /0 × 4

= cos(0) × 0 × 4 /0 × 4

=  1 × 0 × 4 /0 × 4

= 0/0

Since   limx→0 f'(x)/g(x) = 0/0, we differentiate again.

So

limx→0 cos(1 - cos4x) × sin4x × 4 /sin4x × 4  =  limx→0 dcos(1 - cos4x) × sin4x × 4/dx/dsin4x × 4/dx

Let 1 - cos4x = u and 4x = v

1 - cosv = u

limx→0 [d((cosu)/du × du/dv × dv/dx × sinv + cosu dsinv/dv × dv/dx]/du/dv × dv/dx =  limx→0 d((sinu)/du × sinv × 4 ×/sinv × 4

=  limx→0 -sinu × sinv × sinv × 4 + 16cosvcosu /cosv × 4 × 4

=  limx→0 [-4sin(1 - cos4x) × sin²4x + 16cos4xcos(1 - cos4x)]/16cos4x

=  [-4sin(1 - cos4(0)) × sin²4(0) + 16cos4(0)cos(1 - cos4(0))]/16cos4(0)

=  [-4sin(1 - cos(0)) × sin²(0) + 16cos(0)cos(1 - cos(0))]/16cos(0)

=  [-4sin(1 - 1)) × (0) + 16(1)cos(1 - 1)]/16cos(0)

=  [-4sin(0)) × (0) + 16(1)cos(0)]/4cos(0)

=  [-4(0) × (0) + 16(1)(1)]/16(1)

= (0 + 16)/16

= 16/16

= 1

So,  limx→0 ((sin( 1- cos4x))/(1 - cos4x)) = 1

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The answers are given below:

Mean: μ = 60, Standard deviation: σ = 10

Mean: μ = 50, Standard deviation: σ = 8

Mean: μ = 49, Standard deviation: σ = 7.5

For a normal distribution, the empirical rule states:

99.7% of the data is within 3 standard deviations (σ) of the mean (μ)

68% of the data is within 1 standard deviation of the mean

95% of the data is within 2 standard deviations of the mean

99.7% data between 30 and 90:

μ - 3σ = 30, μ + 3σ = 90

Mean: μ = 60, Standard deviation: σ = 10

68% data between 42 and 58:

μ - σ = 42, μ + σ = 58

Mean: μ = 50, Standard deviation: σ = 8

95% data between 34 and 64:

μ - 2σ = 34, μ + 2σ = 64

Mean: μ = 49, Standard deviation: σ = 7.5

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Answer: (-3,-2)

Step-by-step explanation:

 The image of the point (2,−3) under a clockwise rotation of 90° (R_90) about the origin can be found by swapping the x and y-coordinates and changing the sign of the new x-coordinate.

So, the new x-coordinate will be -3 and the new y-coordinate will be -2.

Therefore, the image of the point (2,−3) under a clockwise rotation of 90° (R_90) about the origin is (-3,-2).

The predicted likelihood that Nestor will win at least six of the upcoming races is therefore 90.1%, which is closest to the correct response of -1%.

The likelihood or chance that a specific occurrence or outcome will occur is quantified by probability. It is represented by a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty. For instance, there are two equally likely outcomes (heads or tails), but only one of them is heads, hence the probability of flipping a fair coin and obtaining heads is 0.5 or 50%. By dividing the number of favorable outcomes by the total number of possible outcomes, one can calculate probability.

given

We can see that Nestor won a medal in 6 out of the 10 trials by counting the number of victories.

We can use the binomial distribution with parameters n=10 (number of trials) and p=0.79 to calculate the likelihood that this will occur (probability of success).

The following calculation can be used to determine the likelihood of at least 6 successes in 10 trials:

P(X>=6) = 1 - P(X<=5)

Using a calculator for the binomial distribution, we obtain:

P(X>=6) = 90.1%

The predicted likelihood that Nestor will win at least six of the upcoming races is therefore 90.1%, which is closest to the correct response of -1%.

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The table of value for the given function is written and graphed below

The function s(x) = -0.7x^2 can be evaluated for different values of x to obtain corresponding values of s(x). We can create a table of values for s(x) by choosing a range of x-values and then plugging them into the equation and evaluating.

The table of values for the function s(x) = -0.72x^2 is

x s(x)

-5 -17.5

-4 -11.2

-3 -6.3

-2 -2.8

-1 -0.7

0 0

1 -0.7

2 -2.8

3 -6.3

4 -11.2

5 -17.5

We can use this value to plot a graph using a graphing calculator

Kindly find the attached graph below

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Answer:

Slope = 0.5

Step-by-step explanation:

Slope of a Line passing through two points [tex](x_1 , y_1)[/tex] and [tex](x_2 ,y_2)[/tex] equal [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Since our Line passes through the two points ( -3 , 5 ) and ( 5 , 9 )

Then the Slope = [tex]\frac{9-5}{5-(-3)}=\frac{4}{8} =0.5[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{Slope\ formula\ is :\mathtt{\dfrac{y_2 - y_1}{x_2 - x_1} = slope}\rightarrow \dfrac{rise}{run} = slope}[/tex]

[tex]\textsf{Your labels :}\\\\\mathtt{y_2 \rightarrow 9}\\\mathtt{y_1 \rightarrow 5}\\\\\mathtt{x_2\rightarrow 5}\\\mathtt{x_1\rightarrow-3}[/tex]

[tex]\textsf{Your equation should look like : }\mathtt{slope = \dfrac{9 - 5}{5 - (-3)}}[/tex]

[tex]\textsf{Solving for your answer should be :}[/tex]
[tex]\mathtt{slope = \dfrac{9 - 5}{5 - (-3)}}[/tex]

[tex]\mathtt{slope = \dfrac{9 - 5}{5 + 3}}\\\textsf{(We got a positive (+) symbol because double negatives }(-)\textsf{ make a positive!})[/tex]

[tex]\mathtt{slope = \dfrac{4}{8}}}[/tex]

[tex]\mathtt{slope = \dfrac{4\div2}{8\div2}}[/tex]

[tex]\mathtt{slope = \dfrac{2}{4}}[/tex]

[tex]\mathtt{slope = \dfrac{2\div2}{4\div2}}[/tex]

[tex]\mathtt{slope = \dfrac{1}{2}}[/tex]

[tex]\large\textsf{Thus your \boxed{\textsf{answer}} should most likely be :}\\\\\\\large\boxed{\mathtt{slope = \dfrac{1}{2}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The NBT is used to evaluate a student's academic readiness for tertiary education, whereas the APS is used to establish whether a student meets the minimal standards for admission to a certain course.

What is NBT scores?

The National Benchmark Test Project created the National Benchmark Test (NBT), a test. In order to determine a learner's academic preparation for university, a battery of examinations is utilized to evaluate their academic literacy, general knowledge, and mathematics proficiency.

The NBT pass mark is what?

The National Benchmark Tests do not have a passing score. Your results will be plotted on a benchmark scale, which will help the university determine if you are prepared for university-level work. Since the NBTs are merely a test of preparation for higher education, you cannot pass or fail them.

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Answer:

Step-by-step explanation:

the answer is 38ft^2

Answer:

6 units

Step-by-step explanation:

The area of a triangle is [tex]A = (b \times h)/2[/tex], where b is base and h is height.

In this case, [tex]b = 6[/tex] and [tex]h = x[/tex]. Plug these into the equation:

[tex]18 = (6x)/2[/tex]

[tex]36 = 6x[/tex]

[tex]x = 6[/tex]

Thus, the answer is 6 units.

Hope this helps!

Answer:

y = 3/2x -5

y= 3/2x -7

Step-by-step explanation:

since the two lines are parallel (never touch) they have the same slope, so find the slope of one of the lines (rise over run). Then, to find the y-intercept for the equations, simply look at where each of the lines cross the y-axis.

~lmk if u got Qs

After answering the provided question, we can conclude that As a result, function option A) 5/6 is the correct answer.

A function appears to be a hyperlink between two sets of numbers in mathematics, where each member of the first set (referred as the domain) corresponds to a certain representative of the second set (called the range). In other utterance, a function takes input from a set and produces output by another. Inputs are frequently represented by the variable x, and outputs are represented by the variable y. A function can be represented by a formula or a graph. The method y = 2x + 1 is an example of a conceptual model in which each value assigned to x yields a value of y.

Both Glass A and Glass B initially hold the same amount of liquid. Assume that the total amount of liquid that each glass can hold is equal to 6 units.

As a result, Glass A is initially filled with 3 units of liquid (1/2 of 6 units) and Glass B is initially filled with 2 units of liquid (1/3 of 6 units).

When the liquid from Glass B is poured into Glass A, the total amount of liquid in Glass A increases to 5 units (3 units + 2 units), and the glass is now completely filled.

So, after pouring the liquid from Glass B into it, the fraction of Glass A that is filled is 5/6.

As a result, option A) 5/6 is the correct answer.

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The statement that is NOT true about the frequency chart is "70% of the people spent less than 1 hour watching TV a week".

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The statement that is NOT true about the frequency chart is "70% of the people spent less than 1 hour watching TV a week". This is because according to the table, the percentage of people who spent less than 1 hour watching TV is 50%, which means that half of the people surveyed watched less than 1 hour of TV each week.

Therefore, The statement that is NOT true about the frequency chart is "70% of the people spent less than 1 hour watching TV a week".

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Answer: Slope-intercept form : y-y₁=m(x-x₁)

Passes through (-12, 7)

Slope = -5/3

m = slope

Simply plug everything in :)

y - y₁ = m(x - x₁)

y - 7 = -5/3(x + 12)

Simplify.

y - 7 = -5/3x - 20

Add 7 to both sides.

y = -5/3x = -13

~Hope I helped~

Step-by-step explanation:

The probability that the sample proportion of households spending more than $125 a week is less than 0.32 is 0.3850.

What is probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: A Food Marketing Institute found that 33% of households spend more than $125 a week on groceries. Assume the population proportion is 0.33 and a simple random sample of 349 households is selected from the population.

We have to find the probability that the sample proportion of households spending more than $125 a week is less than 0.32.

P(p < 0.32)

= P(Z < 0.32-0.33 0.33 * 0.67/189

= P(z < -0.29)

= 0.3850

Hence, the probability that the sample proportion of households spending more than $125 a week is less than 0.32 is 0.3850.

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The radius of the circle is 36 centimeters.

A circle's circumference may be divided up into its arcs. Two endpoints and the curve connecting them serve as its definition. The size of the central angle that subtends an arc determines its length. The formula L = r, where L is the length of the arc, r is the radius of the circle, and is the measurement of the central angle in radians, yields the length of an arc in radians. Arcs of circles are utilised in geometry and trigonometry as well as in many other contexts, including creating circular objects and calculating angles.

The length of an arc of a circle is given by the formula:

L = rθ

Given, length of the arc is 32π centimeters and central angle = 8/9π.

Substituting the value we have:

32π = r(8/9π)

r = (32π)/(8/9π)

r = 36

Hence, the radius of the circle is 36 centimeters.

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The complete question is:

Answer:

First, we need to standardize the values using the formula:

z = (x - mu) / sigma

where x is the value, mu is the mean, and sigma is the standard deviation.

For $450: z = (450 - 400) / 50 = 1

For $550: z = (550 - 400) / 50 = 3

Using the 68-95-99.7 rule, we know that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Since we are interested in the probability of a worker making between $450 and $550, we need to find the area under the normal curve between z = 1 and z = 3.

Using a standard normal table or calculator, we can find that the area under the curve between z = 1 and z = 3 is approximately 0.1359.

Therefore, the probability that a worker selected at random makes between $450 and $550 is 13.59% (rounded to two decimal places).

Step-by-step explanation: