Two trains leave stations 494 miles apart at the same time and travel toward each other. One train travels at 100 miles per hour while the other travels at 90
miles per hour. How long will it take for the two trains to meet? do not do any rounding.

Answer:

Step-by-step explanation:

Of the 20 trials, 18 of them ended up between 60 and 75.  So most likely, 60% to 75% of the town rides a bike.

The true statement about the dot plot is (c) Most likely, 60% to 75% of the town rides a bike.

From the dot plot, we have the following sample between 60 and 75%

Sample = 3 + 4 + 6 + 5

Evaluate

Sample = 18

The above means that 18 out of the 20 trials fall between 60 and 75%

This means that between 60 and 75% of the town rides a bike

Hence, the true statement about the dot plot is (c)

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-6b > 36

Final answer:

The minimum cost of production for the company is $260 for 70 dolls.

Explanation:

The minimum cost of production for the company can be determined by examining the options given. The correct statement is:
The minimum cost of production is $260 for 70 dolls.

In the given function, the cost of production is represented by the variable x. The equation cost = 50 + 10x describes the cost of producing x number of dolls. By substituting x with 70 in the equation, we can calculate the cost as follows:

Cost = 50 + 10 * 70 = 50 + 700 = $750

Therefore, the minimum cost of production for the company is $260 for 70 dolls.

Answer:

Part 1: Answer C) There is not enough evidence to reject H0

Part 2: Answer C) There is not enough evidence to accept or reject his claim.

Step-by-step explanation:

Just did it on edge

The z-statistic of 1.41 means the sample mean is 1.41 standard deviations to the right of the population mean, if we assume the null hypothesis is true. The corresponding p-value is approximately 0.1587, which is greater than the commonly used threshold (0.05), leading us to not reject the null hypothesis.

The z-statistic of 1.41 in the sample of Delmar's practice times can be used to draw conclusions about the sample's relationship to the population in a hypothesis test. It represents how many standard deviations an element (or group of elements, like a sample mean) falls from the mean or average of a population. A z-statistic of 1.41 means that the sample mean falls 1.41 standard deviations to the right of the population mean, assuming the null hypothesis to be true.

This information is useful in determining the p-value, which is the probability of observing a test statistic as extreme as the one calculated, assuming that the null hypothesis is true. If the p-value is smaller than the predetermined significance level (let's assume α=0.05), we would reject the null hypothesis. The p-value corresponding to z=1.41 in a two-tailed test is approximately 0.1587. Since this p-value is greater than 0.05, we would not reject the null hypothesis and state that we do not have enough evidence to suggest that Delmar's practice times are significantly different from the population.

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The answer will be D. 7/10 because you have 10 numbers and you want to have a number greater than 3 so it would be 10-3=7 and 7 would go over 10 because there are 7 numbers greater than 3 but less than 10.

The probability he chooses a number greater than 3 is 7/10, the correct option is D.

Probability is the likeliness of an event to happen.

Jalen randomly chooses a number 1-10

Probability = ( No. of favourable outcomes)/ Total Outcomes

The chances of getting the number more than 3 is 7

Total numbers are 10

The probability he chooses a number greater than 3 is 7/10.

Therefore, the correct option is D.

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Answer:

f(x) < –x2 + x – 1

Step-by-step explanation:

The graph is going down so we know that there is a maximum, therefore the A value has to be negative. This rules out f(x) < x2 + x – 1 and f(x) > x2 + x – 1 . The shaded area of the graph is below which indicates that f(x) has to be less than the function. This means the correct answer is f(x) < –x2 + x – 1 .

Answer:

[tex]y>-x^2 +x-1[/tex]

Step-by-step explanation:

Lets find the inequality that best describes the given statement

The graph of the parabola is upside down so the value of 'a' is -1

It means the equation for the parabola becomes [tex]y=-x^2 +x-1[/tex]

Now to get inequality , lets pick a point from the shaded part .

Lets pick (0,0), plug in 0 for x and 0 for y

[tex]y=-x^2 +x-1[/tex]

[tex]0=-(0)^2 +(0)-1[/tex]

[tex]0=-1[/tex]

0 is greater than -1

[tex]y>-x^2 +x-1[/tex]

Answer:

The foci are (2 , 7) and (2 , -3)

Step-by-step explanation:

* lets revise the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (h , k) and transverse axis parallel to the y-axis is

  (y - k)²/a² - (x - h)²/b² = 1

- The coordinates of the vertices are ( h ± a , k )  

- The coordinates of the co-vertices are ( h , k ± b )

- The coordinates of the foci are (h , k ± c), where c² = a² + b²

* Now lets solve the problem

∵ The equation of the hyperbola of vertex (h , k) is

    (y - k)²/a² - (x - h)²/b² = 1

∵ The equation is (y - 2)²/3² - (x - 2)²/4² = 1

∴ k = 2 , h = 2 , a = 3 , b = 4

∵ The foci of it are (h , k + c) and (h , k - c)

- Lets find c from the equation c² = a² + b²

∵ a = 3

∴ a² = 3² = 9

∵ b = 4

∴ b² = 4² = 16

∴ c² = 9 + 16 = 25

∴ c = √25 =  5

- Lets find the foci

∵ The foci are (h , k + c) and (h , k - c)

∵ h = 2 , k = 2 , c = 5

∴ The foci are (2 , 2 + 5) and (2 , 2 - 5)

∴ The foci are (2 , 7) and (2 , -3)

Answer:

The foci are (2 , 7) and (2 , -3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sample is not biased.  The members were selected at random from the gym's female population.

The question is biased.  It described the weight lifting machines as "easy" and the free weights as "harder".

The second and third choices are correct.

Answer:

  9.4 days

Step-by-step explanation:

Filling in the given numbers, we can solve for t:

  0.18 = 1·(1/2)^(t/3.8)

  log(0.18) = (t/3.8)log(1/2)

  t = 3.8·log(0.18)/log(0.50) ≈ 9.4 . . . . days

The best estimate of the age of the sample is 9.4 days.

Answer:

9.4 days

Step-by-step explanation:

[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{15}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{15-8}{9-5}\implies \cfrac{7}{4}[/tex]

Answer:

[tex]AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm[/tex]

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

[tex]AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm[/tex]

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

[tex]\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD[/tex]

Consider right triangle CAH.By the Pythagorean theorem,

[tex]CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8[/tex]

The length cannot be negative, so CD=8 cm and

[tex]CA=\sqrt{3}CD=8\sqrt{3}\ cm[/tex]

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

[tex]AB=2CA=16\sqrt{3}\ cm[/tex]

By the Pythagorean theorem,

[tex]BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm[/tex]

[tex]

y-15=3x \\

-2x+5y=-3 \\ \\

-2x+y-15=0 /\cdot2 \\

-2x+5y-3=0 /\cdot(-2) \\ \\

-4x+2y-30=0 \\

4x-10y+6=0 \\ \\

-8y-24=0 \\

\boxed{y=-3} \\ \\

-3-15=3x \\

\boxed{x=-6}

[/tex]

The answer is C. (-6, -3)

Hope this helps.

r3t40

For this case we have the following system of equations:

[tex]y-15 = 3x\\-2x + 5y = -3[/tex]

We multiply the first equation by -5:

[tex]-5y + 75 = -15x[/tex]

Now we add the equations:

[tex]-2x-5y + 5y + 75 = -3-15x\\-2x + 75 = -3-15x\\-2x + 15x = -75-3\\13x = -78\\x = \frac {-78} {13}\\x = -6[/tex]

We find the value of the variable "y" according to the first equation:

[tex]y = 3x + 15\\y = 3 (-6) +15\\y = -18 + 15\\y = -3[/tex]

The solution of the system is: (-6, -3)

Answer:

(-6, -3)

Option C

You can't in theory. Only a few "nice" values are known, because they lead to particular triangles. For example, we have

You can add other angles using symmetries, for example, you can compute sin(60) using sin(90-x) = cos(x), or similar stuff.

You can also use the double/half angles identities to add another couple of angles in our list, but that's it.

Answer:

  C.

Step-by-step explanation:

The mapping for 90° counterclockwise rotation is ...

  (x, y) ⇒ (-y, x)

If we consider how this applies to points X and Y, which both have a y-coordinate of 0 and a negative x-coordinate, (-a, 0), for example, we see it maps to ...

  (-a, 0) ⇒ (0, -a)

That is, both points X' and Y' will be on the negative y-axis. The only figure showing this is figure C.

______

Comment on the other answer choices

Figures A and D show clockwise rotation. In Figures A and B, the rotation is not about the origin, but is about a different point. (In Figure B, the points easy to consider are the ones on the -x axis, points X and Z. They should appear on the -y axis after rotation, but do not.)

The answer is:

The maximum height before landing will be 69.7804 feet.

Since there is no information about the angle of the launch, we can safely assume that it's launched vertically.

So, we can calculate the maximum height of the pumpkin using the following formulas:

[tex]y=y_o+v_{o}*t-\frac{1}{2}gt^{2}[/tex]

[tex]v=vo-gt[/tex]

Where,

y, is the final height

[tex]y_o[/tex], is the initial height

g, is the acceleration of gravity , and it's equal to:

[tex]g=32.2\frac{ft}{s^{2} }[/tex]

t, is the time.

Now, we are given the following information:

[tex]y_{o}=12ft\\\\v=61\frac{ft}{s}[/tex]

Then, to calculate the maximum height, we must remember that at the maximum height, the speed tends to 0, so, calculating we have:

Time calculation,

We need to use the following equation,

[tex]v=vo-gt[/tex]

So, substituting we have:

[tex]v=61\frac{ft}{s}-32.2\frac{ft}{s^{2}}*t\\\\-61\frac{ft}{s}=-32.2\frac{ft}{s^{2}}*t\\\\t=\frac{-61{ft}{s}}{-32.2\frac{ft}{s^{2}}}=1.8944s[/tex]

We know that it will take 1.8944 seconds to the pumpkin to reach its maximum height.

Maximum height calculation,

Now, calculating the maximum height, we need to use the following equation:

[tex]y=y_o+v_{o}*t-\frac{1}{2}gt^{2}[/tex]

Substituting and calculating, we have:

[tex]y=y_o+v_{o}*t-\frac{1}{2}gt^{2}[/tex]

[tex]y=12ft+61\frac{ft}{s}*1.8944s-\frac{1}{2}32.2\frac{ft}{s^{2}}*(1.8944s)^{2}[/tex]

[tex]y=12ft+61\frac{ft}{s}*1.8944s-\frac{1}{2}32.2\frac{ft}{s^{2}}*(1.8944s)^{2}\\\\y_{max}=12ft+115.5584ft-16.1\frac{ft}{s^{2}}*(3.5887s^{2})\\\\y_{max}=127.5584ft-57.7780ft=69.7804ft[/tex]

Hence, we have that the maximum height before the landing will be 69.7804 feet.

Have a nice day!

Answer:

Use the hyper link

Step-by-step explanation:

I took a picture on the unit.

Answer:

A.The longer leg is √3 times as long as the shorter

B. The hypotenuse is twice as long as the shorter leg

Step-by-step explanation:

The 30-60-90 is a special triangle with two acute angles 30° and 60°

The side across from the 30°= shorter leg

The side across from 60°=longer leg

The side across from 90°=hypotenuse

If we take the shorter side to be x and hypotenuse to be 2x then the  longer leg will be;

Apply Pythagorean relationship

a² + b² =c²

c²-a²=b² where-----------c=2x and a=x

(2x)² - x² = b²

4x² - x² =b²

3x² = b²

√3x²=b

x√3 =b

Hence longer leg is √3 times longer than the shorter leg which is x and the hypothenuse 2x is twice the shorter leg which is x

H(t) = -16t² + vt + s

Where -16 is half of the gravitational constant of almost 32 ft/sec (downward, thus negative),

v is the initial velocity (90), and

s is the starting height (160)

so we have:

H(t) = -16t² + 90t + 160

How long before it hits the ground? Solve for h(t) = 0:

0 = -16t² + 90t + 160

Divide both sides by -2:

0 = 8t² - 45t - 80

Quadratic equation:

t = [ -b ± √(b² - 4ac)] / (2a)

t = [ -(-45) ± √((-45)² - 4(8)(-80))] / (2(8))

t = [ 45 ± √(2025 + 2560)] / 16

t = [ 45 ± √(4585)] / 16

throwing out the negative time:

t = (45 + √4585) / 16

t ≈ 7.04 seconds

ANSWER

[tex] \lim_{x \to \: a}(x) = a[/tex]

[tex]\lim_{x \to \: a}(a) = a[/tex]

[tex]\lim_{x \to \: 5}(x) = 5[/tex]

EXPLANATION

For real number 'a',

[tex] \lim_{x \to \: a}(x) = a[/tex]

is true because we have to plug in 'a' for x.

[tex]\lim_{x \to \: a}(a) = a[/tex]

This is also true because limit of a constant is the constant.

[tex]\lim_{x \to \: 5}(4) = 5[/tex]

is false. The correct value is

[tex]\lim_{x \to \: 5}(4) =4[/tex]

[tex]\lim_{x \to \: 5}(x) = 5[/tex]

is also true because we have to substitute 5 for x.

[tex]\lim_{x \to \: a}(a) = x[/tex]

is also false

The limit should be

[tex]\lim_{x \to \: a}(a) = a[/tex]

Answer:

A, B, D

Step-by-step explanation:

Answers for the rest of the quick check

1. A,B,D

2. 16, D

3. 10a, B

4. 3, D

Good Luck :)

Answer:

x=4

Step-by-step explanation:

16-4=12

3x=12

3*4=12

Answer: [tex]x=4[/tex]

Step-by-step explanation:

You need to find the value of the variable "x".

To solve for "x", the first step is to apply the Subtraction property of equality, which states that:

[tex]If\ a=b\ then\ a-c=b-c[/tex]

Then, you need to subtract 4 from both sides of the equation:

[tex]3x + 4 = 16\\3x + 4-4 = 16-4\\3x=12[/tex]

And finally, you can apply the Division property of equality, which states that:

[tex]If\ a=b\ then\ \frac{a}{c}=\frac{b}{c}[/tex]

Then you can divide both sides of the equation by 3, getting:

[tex]\frac{3x}{3}=\frac{12}{3}\\\\x=4[/tex]

[tex]\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-6}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-6-(-7)}{-8-(-5)}\implies \cfrac{-6+7}{-8+5}\implies \cfrac{1}{-3}\implies -\cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-7)=-\cfrac{1}{3}[x-(-5)]\implies y+7=-\cfrac{1}{3}(x+5)[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_2=m(x-x_2) \\\\ \cline{1-1} \end{array}\implies y-(-6)=-\cfrac{1}{3}[x-(-8)]\implies y+6=-\cfrac{1}{3}(x+8)[/tex]

The graph of inequality have many solution .

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.

According to the question

The system of inequalities:

y ≥ 2x – 4

x + 2y ≤ 7

y ≥ -2

x ≤ 1  

values to the graph of inequalities we will have to make inequalities into equal sign

y ≥ 2x – 4

y = 2x – 4

x                    y

0                  -4

1                   -2

2                  0

Now,

As per graph of inequalities rules:

The solid line for ≤ and ≥.If the symbol ≥ or > is used, shade above the line.

x + 2y ≤ 7

x + 2y = 7

x                    y

0                  3.5

1                   3

2                  2.5

Now,

As per graph of inequalities rules:

The solid line for ≤ and ≥.If the symbol ≤  or < is used, shade below the line.

y ≥ -2

y = -2

Now,

As per graph of inequalities rules:

The solid line for ≤ and ≥.If the symbol ≥ or > is used, shade above the line.

x ≤ 1

x = 1

Now,

As per graph of inequalities rules:

The solid line for ≤ and ≥.If the symbol ≤  or < is used, shade below the line.

Therefore, the darker part in graph  is  common part of all 4 inequalities with point (1,-2) and (1,3) .

Hence, The graph of inequality have many solution .

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Answer:

4 and -4

Step-by-step explanation:

> means greater than

x² > 10

4² > 10 → True, 16 is greater than 10

-4² > 10 → True, 16 is greater than 10

if you add 3 to it it would be 6

Answer:

The answer is the second choice.

Step-by-step explanation:

The value of the domain which is not part of the function is x = -2.

Given data:

The domain of a function is the set of values that are allowed to plug into the function which are the inputs.

The domain of the three line segments is represented as:

Domain of line 1 ranges from [ -5 , -2 ).

Domain of line 2 ranges from ( -2 , 2 ).

Domain of line 3 ranges from [ 2 , 5 ].

So, the value -2 is not included in the domain values of the function.

Hence, x = -2 is not in the domain of function.

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Answer:

  g(10) is undefined

Step-by-step explanation:

A vertical asymptote is a place where a function is literally undefined. That is commonly because the function is a rational function with a denominator of zero at that point (division by zero is undefined), but it can also be for any of a variety of other reasons.

2x+x = 2x^2

X(2+1) = 2x^2

2x^2 stays the same

Therefore the answer is d 3x is not the same as the rest

Answer:

2x^2

Step-by-step explanation:

2x+x=3x

x(2+1)=2x+x=3x

3x

Answer:

Tan <A = 1/2

Step-by-step explanation:

SOH CAH TOA

TOA (opposite/adjacent)

So, the answer is 1/2

because the opposite of <A is 1 and the adjacent is 2.

For this case we have to define trigonometric relations of rectangular triangles, that the tangent of an angle is given by the leg opposite the angle on the leg adjacent to the angle. Then, according to the figure we have:

[tex]tg (A) = \frac {1} {2}[/tex]

Answer:

[tex]tg (A) = \frac {1} {2}[/tex]

Check the picture below.

If these two shapes are combined then the new shape is generated. Then the new shape will be given below.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A cube and a cylinder are given.

If these two shapes are combined then the new shape is generated. Then the new shape will be

The shape is given below.

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Zoe will need 84 pieces if they are 6” by 6”

For this case we have that by definition, 1 foot equals 12 inches.

So:

[tex]3 \ ft = 36 \ in\\7 \ ft = 84 \ in[/tex]

So, the area of the Zoes carpet is:

[tex]A = 36 * 84 = 3024 \ in ^ 2[/tex]

If the cardboard pieces are[tex]6 \ in\ by\ 6 \ in[/tex], then the area is:

[tex]36 \ in ^ 2[/tex]

To indicate the number of necessary pieces we divide:

[tex]\frac {3024} {36} = 84[/tex]

Thus, 84 pieces of cardboard are needed

Answer:

84

Simplify brackets

7 + 1

Simplify

8

Answer: C. 8

Answer:

minus and minus is plus

7+ 1 is 8 :)