Lyle is putting his videotapes on a shelf. The shelf is 12 inches long. If each videotape is 1 1/2 inches wide, how many videotapes can he put side-by-side on the shelf?

Answer:

-2x + 8

Step-by-step explanation:

(2x - 6) is subtracted from (7 - 5).

First term that into an equation.

Because our first term is being subtracted from our second one, our equation is written as:

(7 - 5) - (2x - 6).

Simplify the first term by subtracting:

7 - 5 = 2

Now simplify the second term by multiplying 2x - 6 by -1 to get them out of the parenthesis. We do this because there is a negative sign in front of it.

-1 (2x - 6)

-2x + 6

Now our equation is:

2 - 2x + 6

Combine like terms:

2 + 6 = 8

So -2x + 8

(2x - 6) subtracted from (7 - 5) is -2x+8

Answer:

B

Step-by-step explanation:

I hope it helps :)

Answer:

Step-by-step explanation:

y=4/3 x +b

goes through the point (1,3)

3=4/3(1)+b

b=3-4/3

b=9-4/3

b=5/3

equation : y=4/3 x +5/3

The graph of the line with slope of 4/3 and goes through the point (1,3) is shown in attached figure.

What is Equation of line?

The equation of line with slope m and passes through the point (x₁, y₁) is given as;

y - y₁ = m (x - x₁)

Given that;

The slope of line = 4/3

And, Point on line = (1, 3)

Since, The equation of line with slope m and passes through the point (x₁, y₁) is given as;

y - y₁ = m (x - x₁)

Thus, The equation of line with slope 4/3 and passes through the point (1, 3) is given as;

y - 3 = 4/3 (x - 1)

Solve as;

3 (y - 3) = 4 (x - 1)

3y - 9 = 4x - 4

3y = 4x - 4 + 9

3y = 4x + 5

y = 4/3x + 5/3

Thus, The equation of line will be;

y = 4/3x + 5/3

So, The graph of the line y = 4/3x + 5/3 is shown in attached figure.

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Answer:

30.4

Step-by-step explanation:

17+28+32+35+59+20+19+33+30+31=304

304/10=30.4

a and c are directly proportional to each other when a and b are directly proportional and b and c are directly proportional.

If a and b are directly proportional and b and c are directly proportional, it means that their ratios are equal. Direct proportionality implies that as one variable increases, the other also increases in proportion and as one variable decreases, the other also decreases in proportion.

Mathematically, this can be written as

a = kb and b = mc, where k and m are constants of proportionality.

Multiplying these two equations gives: a = kbm

Substituting the value of b from the second equation in the first equation, we get: a = kmc

Therefore, a and c are also directly proportional to each other with a constant of proportionality km.

Thus, if a increases by a certain factor, c will also increase by the same factor.

If a and b are directly proportional and b and c are directly proportional, then it can be concluded that a and c are directly proportional as well.

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Given statement solution is :- The set of ordered pairs (-1, -3) and (5, 5) determine a line with a slope of 4/3, according to the given statement's answer.

To determine the slope of a line given two ordered pairs (x1, y1) and (x2, y2), we use the formula:

slope is equal to y2 - y1 / x2 - x1.

Let's calculate the slopes for each set of ordered pairs:

A. (5, -3) (2, 3)

slope = (3 - (-3)) / (2 - 5)

= 6 / (-3)

= -2

B. (3, 10) (-3, -2)

slope = (-2 - 10) / (-3 - 3)

= -12 / (-6)

= 2

C. (3, -5) (-3, -7)

slope = (-7 - (-5)) / (-3 - 3)

= (-2) / (-6)

= 1/3

D. (-1, -3) (5, 5)

slope = (5 - (-3)) / (5 - (-1))

= 8 / 6

= 4/3

Option D's set of ordered pairs, (-1, -3) and (5, 5), results in a line with a slope of 4/3.

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Answer:

Step-by-step explanation:

x = -2

F(x)=1.5(2)^x=0.375 , G(x)=-3(1/4)^x=-48

x=0

F(x)=1.5(2)^x=3, G(x)=-3(1/4)^x=-3

x=1/2

F(x)=1.5(2)^x=1.06 , G(x)=-3(1/4)^x=-6

Answer:

382.5 Inches

Step-by-step explanation:

Hope this helped

Answer:

382.5

Step-by-step explanation:

1 1/5 × 5,+ 5× 3

hope you got that lol

A student is not correct when he stated that a triangle can be formed with side lengths 3 in, 5 in, and 9 in because 3 + 5 < 9.

A triangle is a polygon with three sides and three vertices.

To know if a set of numbers is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 3, b = 5, and c = 9

a + b > c : 3 + 5 > 9     8 > 9     False

a + c > b : 3 + 9 > 5     12 > 5     True

b + c > a : 5 + 9 > 3     14 > 3     True

If at least one of these statements does not hold true, the measurements can't be the sides of a triangle.

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The probability that this whole shipment will be accepted is 0.1813. The company will accept 82.87% of the shipments and will reject 17.13% of the shipments, so the likelihood of a rejected shipment is relatively low.

Probability is essentially the likelihood that something will occur. The entire number of potential outcomes must first be known in order to calculate the likelihood of a particular event.

P(E) = Number of favorable outcomes / Number of total outcomes

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Answer:

.78 cents

Step-by-step explanation:

To find the tax amount on any number, divide that number by 100 and then multiple it by the tax percentage.

In this case that would look like: $19.50/100 times 4 =.78

He must purchase 3 packages of hot dogs and 2 packages of hot dog buns for a total of 24 hot dogs with buns if he doesn't want to have any leftover hot dogs or buns. You should be aware that students might respond with 24, which is the least common multiple of 8 and 12.

The hot dog buns most frequently used in the American region of New England and its cuisine are New England-style hot dog buns, also referred to as New England hot dog buns or top-loading hot dog buns.

As you can see, "hot dog" is a versatile word that can be used as a noun, verb, adjective, or even as an exclamation.

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Answer:thus the answer is 2

Step-by-step explanation:

Given

The Radius of a solid cylinder (r)=5cm

Height (h)=10cm

Hence

Total surface area =2πrh+2πr

2

=2πr(h+r)

=2π×5(10+5)

=π×10×15

=150πcm

2

Figure (c) is a dilation of figure ABCD.

By drawing rays from point Q to each of the vertices of figure ABCD and extending them to intersect with a new figure, we may determine the dilation since figure ABCD is dilated from point Q.

Looking at the possible answers, we can see that only figure (c), with all angles and side lengths proportional to those in ABCD, has the same form as ABCD. Figure (c) shows a dilatation of Figure ABCD as a result.

As figure (c) exceeds ABCD, the dilation has a scale factor higher than 1. In other words, the ratio of the corresponding side lengths is the same for all sides, and each side length and angle in figure (c) are larger than the corresponding side length and angle in ABCD.

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A significance level of 0.05, the critical value for the right-tailed test is z = 1.645.

To test if the data provides enough evidence to conclude that the cream improved the skin of more than 60% of the women, we can conduct a hypothesis test.

Let p be the true proportion of middle-aged women who show skin improvement after using the anti-aging skin cream.

The null hypothesis is: H0: p ≤ 0.6

The alternative hypothesis is: Ha: p > 0.6

We can use a one-tailed z-test for proportions to test this hypothesis, where the test statistic is given by:

z = (P - p0) / sqrt(p0 * (1 - p0) / n)

where P is the sample proportion, p0 = 0.6 is the null hypothesis value, and n = 33 is the sample size.

From the table, we see that 26 out of 33 women showed skin improvement after using the cream. Therefore, the sample proportion is:

P = 26 / 33 = 0.7879

Substituting the values, we get:

z = (0.7879 - 0.6) / sqrt(0.6 * 0.4 / 33) = 2.162

Using a significance level of 0.05, the critical value for the right-tailed test is z = 1.645.

Since the calculated test statistic (z = 2.162) is greater than the critical value (z = 1.645), we reject the null hypothesis and conclude that there is enough evidence to suggest that the cream improved the skin of more than 60% of the women.

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Answer:

922,500,000

Step-by-step explanation:

9.225 x 10 to the 8th Power Equals

922,500,000

Hope this helps!!

Answer:

Both.

Step-by-step explanation:

Answer:

both

Step-by-step explanation:

guy above me is right

Two sides should be equal and the angle between the corresponding equal sides should needed be equal prove that the triangles are congruent using SAS congruent rule.

Given, two triangles and we have to prove that the triangles are congruent using SAS.

Also, we are asked the information needed to prove that the triangles are congruent using SAS.

Using the concept of Congruent Triangles,

SAS stands for Side- Angle-Side

To prove that two triangles are congruent by SAS Congruent Rule,

Two corresponding sides of the triangles should be equal and the angle between the sides should also be equal.

Then, we can prove that the triangles are congruent using SAS Congruent Rule.

Let suppose ABC and XYZ are two triangles,

AB = XY

∠ABC = ∠XYZ

BC = YZ

So, by SAS congruent rule ΔABC ≅ ΔXYZ.

Hence, two sides and one angle is needed to prove that the triangles are congruent using SAS congruent rule.

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The exact values of all angles in the interval [0, 360°) that satisfy the given equations are:

data = 45°, 135°, 315°.

To solve the given trigonometric equations, we will consider each equation separately.

tan²(data) - 1 = 0:

First, let's rewrite tan²(data) as (sin(data)/cos(data))²:

(sin(data)/cos(data))² - 1 = 0

Now, we can factor the equation:

(sin²(data) - cos²(data)) / cos²(data) = 0

Using the Pythagorean identity sin²(data) + cos²(data) = 1, we can substitute sin²(data) with 1 - cos²(data):

((1 - cos²(data)) - cos²(data)) / cos²(data) = 0

Simplifying further:

1 - 2cos²(data) = 0

Rearranging the equation:

2cos²(data) - 1 = 0

Now, we solve for cos(data):

cos²(data) = 1/2

cos(data) = ± √(1/2)

cos(data) = ± 1/√2

cos(data) = ± 1/√2 * √2/√2

cos(data) = ± √2/2

From the unit circle, we know that cos(data) = √2/2 corresponds to angles 45° and 315° in the interval [0, 360°). Therefore, the solutions for data are:

data = 45° and data = 315°.

cos(data)sin(data) = 1:

Since cos(data) ≠ 0 (otherwise the equation wouldn't hold), we can divide both sides by cos(data):

sin(data) = 1/cos(data)

sin(data) = 1/√2

From the unit circle, we know that sin(data) = 1/√2 corresponds to angles 45° and 135° in the interval [0, 360°). Therefore, the solutions for data are:

data = 45° and data = 135°.

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The optimal clutch size is 1.

a)The survivorship of an offspring, S, decreases with the clutch size, C.

Therefore, the formula is given as:

S = 0.5 - 0.1C

We need to find the optimal clutch size for this bird species.

We can do this by differentiating S with respect to C, and equating the result to zero.

That is:S = 0.5 - 0.1C => dS/dC = -0.1

Equating dS/dC to zero gives:-0.1 = 0 => C = 0

This implies that there is no optimal clutch size for this species.

However, since C represents clutch size, it must be a positive integer.

Therefore, we can choose a clutch size of 1, which will result in the highest survivorship of offspring. Hence, the optimal clutch size is

1.b)The optimal clutch size for a species with a survivorship-clutch size relationship of the form S = a - bC can be obtained by following the same procedure as above.

We can differentiate S with respect to C, and equate the result to zero.

That is:S = a - bC => dS/dC = -b

Equating dS/dC to zero gives:-b = 0 => C = 0

This implies that there is no optimal clutch size for this species. However, since C represents clutch size, it must be a positive integer. Therefore, we can choose a clutch size of 1, which will result in the highest survivorship of offspring. Hence, the optimal clutch size is 1.

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According to the ratio, it doesn't make sense to have a total of 9 people in the dance competition.

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

The ratio of boys to every girls is 3:2 in a dance competition.

Let's find if it will make sense to have a total of 9 people in the competition.

Therefore,

number of boys = 3 / 5 × 9 = 27 / 5 = 5.4

number of girls = 2 / 5 × 9 = 18 / 5 = 3.6

Therefore, it doesn't make sense to have 9 people in the competition because the actual number of boys and girls will be in decimal which is impossible.

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Answer:

Part A is 11 I think

Step-by-step explanation:

Answer:thank you

Step-by-step explanation:

There you go I hope its correct

Yes, it is true that if A and B are square and invertible matrices, then AB is also invertible, and its inverse is given by\((AB)^{(-1) }= B^{(-1)}A^{(-1).\)

To see why this is true, consider the product\((AB)(B^{(-1)}A^{(-1)}).\)

Using the associative property of matrix multiplication, we can rearrange this expression as

\((A(BB^{(-1)})A^{(-1)}) = (AIA^{(-1)}) = AA^{(-1)} = I,\)

where I is the identity matrix.

Similarly, we can show that \((B^{(-1)}A^{(-1)})(AB) = I,\) which means that

\((AB)^{(-1) }= B^{(-1)}A^{(-1).\)

Therefore, we conclude that if A and B are square and invertible matrices, then AB is invertible, and its inverse is given by \((AB)^{(-1)} = B^{(-1)}A^{(-1).\)

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The only pair of events that are independent among the three given pairs is the one where the probability of A is 0.6, the probability of B is 0.4, and the probability of the intersection of A and B is 0.24.

Pairs of events that are independent have probabilities that are not affected by the occurrence or non-occurrence of the other event. In other words, if A and B are independent events, then the probability of A occurring does not change based on whether or not B occurs, and vice versa.

To determine which pairs of events are independent, we need to calculate the probability of each event occurring and the probability of their intersection. If the probabilities satisfy the formula P(A ∩ B) = P(A)P(B), then the events are independent.

For the given pairs of events, we have:

P(A) = .40, P(B) = .60, P(A ∩ B) = .14. These events are not independent because P(A ∩ B) ≠ P(A)P(B) (.14 ≠ .24).

P(A) = .60, P(B) = .40, P(A ∩ B) = .24. These events are independent because P(A ∩ B) = P(A)P(B) (.24 = .24).

P(A) = .70, P(B) = .40, P(A ∩ B) = .28. These events are not independent because P(A ∩ B) ≠ P(A)P(B) (.28 ≠ .28).

Therefore, the pair of events that are independent is P(A) = .60, P(B) = .40, and (A ∩ B) = .24.

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Answer:

Car insurance. You pay monthly, hoping that you never get into a crash. If you do, it pays for repairing or replacing your car, and/or the other car/s involved.

Routine maintenance. Every 35,000 miles driven (or so), you need new tires. Every 3-5,000 miles driven, you need to get the oil changed. You need to replace brake pads, windshield wipers, etc.

Gasoline. The price varies, and depending on how big your car's engine and gas tank is, that can get very expensive.

Unplanned repairs. Dead battery, car overheats. You have to get the car fixed so you can get to work/school.

The given ratio of yes votes to no votes is 3:4

Then,

The ratio of yes votes: to no votes = 3:4  

Yes votes = 2721,

Now,

2721/3 = 907

907 × 4 = 3628.

Hence, there were 3628 no votes.

To calculate the ratio, use this formula:

Ratios equate two numbers, usually by dividing them. If you are comparing one data point (x) to any other data point (y), your formula would be x/y. This means you are dividing information x by information y.

For example, if A is 50 and B is 100, your ratio will be 50/100 the ratio will be 1:2.

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Answer:

Slope: 1/4

Step-by-step explanation:

The slope formula is rise/run.

Find the two points at which the line crosses.

Hope this helps :)

Tips: To find the slope, you can find the change in y over the change in x. Pick any two points on the line, for example: (0,3) and (4,4). To find the change in y, take the y value of one ordered pair and subtract it from the other. Then take this value and divide it by the difference of the corresponding x values.

ex:

4-3/4-0

slope: 1/4

You can also count the “rise” over “run” from (0,3). You can see that you move up 1 unit and right 4 units to get to (4,4), meaning the slope is 1/4 (rise 1, run 4)

Answer:

67°.

Step-by-step explanation:

1) m∠PMR=m∠LMN=3x+19°;

2) m∠LMN+m∠LMP=180°, it can be written as 3x+19+9x-31=180;

3) if to solve the equation 3x+19+9x-31=180, then x=16;

4) m∠PMR=3x+19=48+19=67°.

x = 5pi/6 is not in the interval [0, pi/2]

Starting with the given equation:

4 cos x - 8 sin x cos x = 0

We can factor out 4 cos x:

4 cos x (1 - 2 sin x) = 0

So either cos x = 0 or (1 - 2 sin x) = 0.

If cos x = 0, then x = pi/2 since we're only considering the interval [0, pi/2].

If 1 - 2 sin x = 0, then sin x = 1/2, which means x = pi/6 or x = 5pi/6 in the interval [0, pi/2].

So the two solutions in the interval [0, pi/2] are x = pi/2 and x = pi/6.

That x = 5pi/6 is not in the interval [0, pi/2].

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The given equation is 4 cos x - 8 sin x cos x = 0. To find the solutions in the interval [0, pi/2], we need to solve for x.
Find the solutions within the given interval. Equation: 4 cos x - 8 sin x cos x = 0

First, let's factor out the common term, which is cos x:

cos x (4 - 8 sin x) = 0

Now, we have two cases to find the solutions:

Case 1: cos x = 0
In the interval [0, π/2], cos x is never equal to 0, so there is no solution for this case.

Case 2: 4 - 8 sin x = 0
Now, we'll solve for sin x:

8 sin x = 4
sin x = 4/8
sin x = 1/2

We know that in the interval [0, π/2], sin x = 1/2 has one solution, which is x = π/6.

So, in the given interval [0, π/2], the equation has only one solution: x = π/6.

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