Wayne counts the bikes and cars in the school parking lot. There are 13 bikes and 98 cars. Which equation can be used to find t, the number of tires in the parking lot?

(13×4)+(3×t)=98

98−(13×2)=(4+t)

(13×2)+(98×4)=t

98÷(13×2)=(4×t)

Answer:

To analyze the function H(x) = -x^2 - 6x - 16, we can start by finding its vertex and intercepts:

Vertex: The x-coordinate of the vertex of the parabola represented by H(x) is given by x = -b/2a, where a and b are the coefficients of x^2 and x, respectively. In this case, a = -1 and b = -6, so x = -(-6)/2(-1) = 3. To find the corresponding y-coordinate, we substitute x = 3 into H(x) and get:

H(3) = -(3)^2 - 6(3) - 16 = -25

Therefore, the vertex of H(x) is (3, -25).

y-intercept: To find the y-intercept, we set x = 0 in H(x) and get:

H(0) = -(0)^2 - 6(0) - 16 = -16

Therefore, the y-intercept is (0, -16).

x-intercepts: To find the x-intercepts, we set H(x) = 0 and solve for x:

-x^2 - 6x - 16 = 0

Multiplying both sides by -1 and rearranging, we get:

x^2 + 6x + 16 = 0

Using the quadratic formula, we get:

x = (-6 ± √(6^2 - 4(1)(16))) / (2(1)) = (-6 ± 2√5i) / 2 = -3 ± √5i

Therefore, the x-intercepts are (-3 + √5i, 0) and (-3 - √5i, 0).

Axis of symmetry: The axis of symmetry is the vertical line passing through the vertex, which is x = 3 in this case.

Direction of opening: Since the coefficient of x^2 is negative, the parabola opens downwards.

Maximum value: Since the parabola opens downwards, the vertex represents the maximum point of the function. Therefore, the maximum value of H(x) is -25.

With this information, we can sketch the graph of H(x), which looks like a downward-facing parabola with vertex at (3, -25), x-intercepts at (-3 + √5i, 0) and (-3 - √5i, 0), and y-intercept at (0, -16).

Answer:

100000

Hope this helps

If an event occurs 0 times (out of 4, in this case) then it does not occur at least once. So we can find the probability of it not occurring and then subtract that value from 1.

So, what are the chances of it not occurring in 1 trip?

1−.37=.63

What about not occurring in 2 trips?

(1−.37)⋅(1−.37)=.63⋅.63=.3969

Now what about not occurring in 4 trips?

.63^4 = 0.15752961

We must subtract this value from 1

(recall that what we just calculated is the probability of it not occurring, so the probability of it occurring at least once is:

1−0.15752961 = .84247039

TLDR - In 4 trips the chance of a guest catching a cutthroat once in under 4 trips in 0.84.

Answer:

The simplified answer to that is -0.2x.

Hope this helps and if you could mark this as brainliest. Thanks!

Answer:

-0.2x

Step-by-step explanation:

If x is negative then,

-0.2(-2) = 0.4

Answer:

B

Step-by-step explanation:

\(3\sqrt{5}\)

Step-by-step explanation:

x + 7- 5x- 5

= x - 5x +7- 5

= -4x + 2

= -2 (2x - 1)

Answer:

-4x+2

Step-by-step explanation:

Combine Like Terms:

x + 7 - 5x - 5

-4x + 7 - 5

-4x + 2

The measure of CFD is 66°.

It should be noted that vertically opposite angles are equal.

Therefore, AFE may be equal to BFD.

In this case, AFE is given as 108° while one of the other angles is given as 42°.

Therefore, the value of CFD will be:

= 102° - 42°

= 66°

The value of CFD is 66°.

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Part A: The range shown in the  of pets can be determined by examining the box-and-whisker plot. However, since the plot is not provided in the question, I am unable to provide an exact answer.

Part B: Similarly, the range of the middle 50% of the average life span of pets cannot be determined without the box-and-whisker plot.

Part C: Without the box-and-whisker plot or any specific data, it is not possible to determine which quartile has the largest spread of life spans.

The spread of life spans within each quartile can be identified by analyzing the interquartile range (IQR), but since the plot or specific data is not available, we cannot make any conclusions about the quartile with the largest spread.

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Best way to solve this is by using

\( \sqrt{s(s - a)(s - b)(s - c)} \)

\(where \: s = \frac{a + b + c}{2} \)

s=(12+8+17)/2

=18.5

using the formulae

area =43.5

The resulting atom when a nuclide of superscript 64 subscript 29 upper c u. absorbs a positron is; Superscript 64 subscript 30 upper Z n.

A positron is the anti-particle of a beta particle and it is emitted by a proton-rich nucleus.

Now, the collision of an electron and a positron yields two 0.511 MeV gamma rays because Positron gamma radiation can penetrate through inches of very hard material.

Thus, the resulting atom when a nuclide of superscript 64 subscript 29 upper c u. absorbs a positron is; Superscript 64 subscript 30 upper Z n.

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Therefore ,there are 158,184,000 ways to create a license plate in this system.

A selection from a group of separate items is called a combination in mathematics, and the order in which the elements are chosen is irrelevant (unlike permutations). An apple and a pear, an apple and an orange, or a pear and an orange are three combinations of two fruits that can be chosen from a set of three fruits, such as an apple, an orange, and a pear. Formally speaking, a set S's k-combination is a subset of S's k unique components. Two combinations are therefore equal if and only if they have the same elements in both combinations.

According to the counting principle, the total number of ways to obtain a license plate is calculated by multiplying the number of times each of these events might occur together.

The first number (the digits 1 through 9) can be obtained in nine different ways.

There are 26 methods to obtain the first letter. There are 26 ways to obtain the following letter (repetition is acceptable).

There are 26 methods to get the third letter, 10 ways to get the next number (zero is acceptable), and 10 ways to get the following number with repetitions.

How many ways are there to get the next number? 10 ways\s.

Thus ,total options for obtaining a license plate:

9 x 26 x 26 x 26 x 10 x 10=158184000

Therefore ,there are 158,184,000 ways to create a license plate in this system.

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Answer:

(-6, 4)

Step-by-step explanation:

Given the coordinate points (-3,1). If The point (-3,1) is moved 3 places in the negative y direction and 2 places in the positive x direction the required coordinate will be expressed ss;

X' = (-3-3, 1+3)

X = (-6, 4)

Hence the resulting coordinate will be at:(-6, 4)

Based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

To solve the problem using the determinant method (Cramer's rule), we need to set up a system of equations based on the given information and then solve for the unknowns, which represent the number of 0.5 litre bottles and 0.7 litre bottles.

Let's denote the number of 0.5 litre bottles as x and the number of 0.7 litre bottles as y.

From the given information, we can set up the following equations:

Equation 1: 0.5x + 0.7y = 16.5 (total volume of moonshine)

Equation 2: 8x + 10y = 246 (total earnings from selling moonshine)

We now have a system of linear equations. To solve it using Cramer's rule, we'll find the determinants of various matrices.

Let's calculate the determinants:

D = determinant of the coefficient matrix

Dx = determinant of the matrix obtained by replacing the x column with the constants

Dy = determinant of the matrix obtained by replacing the y column with the constants

Using Cramer's rule, we can find the values of x and y:

x = Dx / D

y = Dy / D

Now, let's calculate the determinants:

D = (0.5)(10) - (0.7)(8) = -1.6

Dx = (16.5)(10) - (0.7)(246) = 150

Dy = (0.5)(246) - (16.5)(8) = -18

Finally, we can calculate the values of x and y:

x = Dx / D = 150 / (-1.6) = -93.75

y = Dy / D = -18 / (-1.6) = 11.25

However, it doesn't make sense to have negative quantities of bottles. So, we can round the values of x and y to the nearest whole number:

x ≈ -94 (rounded to -94)

y ≈ 11 (rounded to 11)

Therefore, based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

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Question

Matti is making moonshine in the woods behind his house. He’s selling the moonshine in two different sized bottles: 0.5 litres and 0.7 litres. The price he asks for a 0.5 litre bottle is 8€, for a 0.7 litre bottle 10€. The last patch of moonshine was 16.5 litres, all of which Matti sold. By doing that, he earned 246 euros. How many 0.5 litre bottles and how many 0.7 litre bottles were there? Solve the problem by using the determinant method (a.k.a. Cramer’s rule).

The measure of the angle ABC from the diagram is equivalent to 78 degrees.

We need to find <ABC

Let us produce BA to meet PR at point G.

It is given that BG || PQ

Thus, <RGB and <QPR are corresponding angles.

This shows that <RGB = <QPR since they are corresponding angles.

On the other hand, <QPR = 102 degrees and <ABC are <RGB consecutive interior angles, then:

<ABC + <RGB = 180

<ABC + 102 = 180

<ABC = 180 - 102

<ABC = 78 degrees

Hence the measure of the angle ABC from the diagram is 78 degrees.

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Approximately 34.13% of men in the Dinaric Alps region have a height between 68 and 72 inches.

To calculate this percentage, we need to find the area under the normal distribution curve between 68 and 72 inches. We can do this by standardizing the values using the z-score formula:

z = (x - μ) / σ

where x is the height value, μ is the mean height, and σ is the standard deviation.

For x = 68 inches, the z-score is:

z = (68 - 73) / 3 = -1.67

For x = 72 inches, the z-score is:

z = (72 - 73) / 3 = -0.33

Using a standard normal distribution table or a calculator with a normal distribution function, we can find that the area under the curve between z = -1.67 and z = -0.33 is approximately 0.3413 or 34.13%. Therefore, approximately 34.13% of men in the Dinaric Alps region have a height between 68 and 72 inches.

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To identify the vertical asymptotes, we have to factor the denominator. For horizontal asymptotes, we compare the degrees of the numerator and denominator.

For rational functions, there are vertical and horizontal asymptotes. To identify the vertical asymptotes, we first have to factor the denominator. After that, we should look for values that make the denominator zero. These values can be found by setting the denominator equal to zero and solving for x. The resulting x values would be the vertical asymptotes of the function.

The horizontal asymptote is the line that the function approaches as x goes towards infinity or negative infinity. For rational functions, the horizontal asymptote is found by comparing the degrees of the numerator and the denominator.

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is y = the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

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The factored form of the quadratic equation is given as follows:

y = 3(x + 0.6667)(x - 6).

The quadratic equation for this problem is defined as follows:

3x² - 16x - 7 = 5.

3x² - 16x - 12 = 0.

The coefficients are given as follows:

a = 3, b = -16, c = -12.

Hence the discriminant is of:

D = (-16)² - 4(3)(-12)

D = 400.

Then the roots are of:

Considering the leading coefficient of 3 and the roots, the factored form of the equation is given as follows:

y = 3(x + 0.6667)(x - 6).

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If the cross-price elasticity of demand for two goods is 1.25, then the two goods are substitutes.

Cross Price Elasticity of Demand:

The cross elasticity of demand is an economic concept that measures the response of the quantity demanded of one good to changes in the price of another good. Also known as the cross-price elasticity of demand, this measure is calculated by dividing the percentage change in quantity demanded for one good by the percentage change in price of another commodity.

\(E_X_Y\) = \(\frac{Percentage change in Quantity of X }{Percentage Change in Quantity of Y}\)

\(E_X_Y\) = ΔQ/Q ÷ ΔP/P

       = ΔQ/Q × P/ΔP

       = ΔQ/ΔP × P/Q

where:

Q = Quantity of good X

P = Price of good Y

Δ = Change

​The cross elasticity of demand for a substitute is always positive because an increase in the price of a substitute increases the demand for one good. For example, when the price of coffee rises, the demand for tea (alternative beverage) increases as consumers switch to cheaper but alternative beverages. This is reflected in the formula for the cross-elasticity of demand, as the numerator (the percentage change in demand for tea) and the denominator (the price of coffee) represent positive increases.

Items with a coefficient of 0 are unrelated and independent products. Commodities can be weak substitutes for which both products are positive but have a low cross-elasticity of demand. This is often the case with various alternative products such as tea or coffee. Commodities that are strong substitutes have a higher cross-elasticity of demand. Consider a different brand of tea. An increase in the price of green tea from one company has a greater impact on the demand for green tea from the other company.

The cross elasticity of demand is 1.25. Positive cross elasticity means that when the price of one good changes, the quantity demanded of another good changes in the same direction. For example, when the price of one good increases, the demand for another good increases.

This indicates that the two products are fungible. When the price of a product rises, consumers will prefer the cheaper product. As a result, the demand for alternatives will increase.

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Answer: To determine the break-even quantity, we need to find the point where the revenue equals the cost. In other words, we need to solve the equation R(x) = C(x).

Given:

Setting R(x) = C(x), we have:

Subtracting 135x from both sides of the equation:

Simplifying the left side:

Dividing both sides by 45:

The break-even quantity is 1,236 units.

Since the break-even quantity (1,236 units) is less than the maximum number of units that can be sold (2,097 units), the firm can produce the product because it would make money.

To determine the break-even quantity and decide whether to proceed with the production of the new product, we need to analyze the cost and revenue data provided.

The cost function is given as C(x) = 135x + 55,620, where x represents the quantity of units produced. The revenue function is given as R(x) = 180x. To break even, the total cost and total revenue should be equal. We can set up an equation based on this condition: C(x) = R(x). Substituting the given cost and revenue functions: 135x + 55,620 = 180x

To solve for x, we can subtract 135x from both sides: 55,620 = 45x. Now, divide both sides by 45: x = 1,236. The break-even quantity is 1,236 units.

Since the number of units that can be sold is no more than 2,097 units, which is greater than the break-even quantity of 1,236 units, the firm can produce the product. The break-even point indicates the minimum number of units that need to be sold to cover the costs, and since the firm can sell more than the break-even quantity, it has the potential to make a profit. However, further analysis of other factors such as market demand, competition, and potential profitability should also be considered before making a final decision.

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Answer:

-1.5 + 4.2

Step-by-step explanation:

Since there is no negative sign,the sign would change.

So it will be -1.5+4.2

The sum of the first four terms of the sequence is 22.

In this question,

The formula of sum of linear sequence is

\(S_n =\frac{n}{2}(2a+(n-1)d)\)

The sum of the first ten terms of a linear sequence is 145

⇒ \(S_{10} =\frac{10}{2}(2a+(10-1)d)\)

⇒ 145 = 5 (2a+9d)

⇒ \(\frac{145}{5} =2a+9d\)

⇒ 29 = 2a + 9d  ------- (1)

The sum of the next ten term is 445, so the sum of first twenty terms is

⇒ 145 + 445

⇒ \(S_{20} =\frac{20}{2}(2a+(20-1)d)\)

⇒ 590 = 10 (2a + 19d)

⇒ \(\frac{590}{10}=2a+19d\)

⇒ 59 = 2a + 19d -------- (2)

Now subtract (2) from (1),

⇒ 30 = 10d

⇒ d = \(\frac{30}{10}\)

⇒ d = 3

Substitute d in (1), we get

⇒ 29 = 2a + 9(3)

⇒ 29 = 2a + 27

⇒ 29 - 27 = 2a

⇒ 2 = 2a

⇒ a = \(\frac{2}{2}\)

⇒ a = 1

Thus, sum of first four terms is

⇒ \(S_4 =\frac{4}{2}(2(1)+(4-1)(3))\)

⇒ \(S_4 =2(2+(3)(3))\)

⇒ S₄ = 2(2+9)

⇒ S₄ = 2(11)

⇒ S₄ = 22.

Hence we can conclude that the sum of the first four terms of the sequence is 22.

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Answer:

Step-by-step explanation:

Starting elevation of B = +200 feet

Change in elevation for B = 75 feet down

Final elevation of B = +200 - 75 = +125 feet

The addition equation for B can be written as:

Starting elevation + Change = Final elevation

+200 - 75 = +125

The number line diagram for B is as follows:

+------------------------+------------------------+------------------------+

A B C D

+200 +125 +225

<----- 75 ft ----->

(change in elevation)

Answer:

a=15

Step-by-step explanation:

Pythagorean Theorum says that a²+b²=c², so if we square b and c, subtract b² from c², and then square root that answer, it will equal a.

a²+8²=17²

8²=64

17²=225

225-64=225

√225=15

Answer:

yes they can

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

yes they can............

Answer:

Perimeter of the final star = 40 cm²

Step-by-step Explanation:

The perimeter of the six-pointed star is the sum of the sides of the 6 equilateral triangles that form a boundary around the star.

1 triangular tiles gas a perimeter of 10cm.

Only 2 out of the 3 equal sides of each of the 6 equilateral triangles form the boundary of the final star.

Therefore, perimeter of the final star = ⅔ of the total perimeter of 6 triangular tiles

= ⅔ of (10*6)

= ⅔*60

= 2*20

Perimeter of the final star = 40 cm²

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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Answer:

the answer is 3/28

Step-by-step explanation:

Answer:

There is no picture, my sweetheart.

Step-by-step explanation: