A: An ice cream factory makes 120 quarts of ice cream in 10 hours.

What was the rate per hour?

B: The ratio of wooden bats to metal bats in the baseball coach’s bag is
2 to 1. If there are 20 wooden bats, how many metal bats are in the
Bag?

Answer:

2. -1/2

4. 3/2

Step-by-step explanation:

Gradient = (Y1 - Y2)/(X1 - X2)

2.

Point 1: (4, -1)

Point 2: (-2, 2)

Gradient = (-1 - 2)/(4 - (-2)) = -3/6 = -1/2

3.

Point 1: (4, 6)

Point 2: (-4, -6)

Gradient = (6 - (-6))/(4 - (-4)) = 12/8 = 3/2

Answer:

Additive inverse is -2

Multiplicative inverse is 1/2

Answer:

2 is an integer then the multiplicative inverse of 2 is \[\dfrac{1}{2}\]. Hence, we obtained the additive inverse of 2 is -2 and the multiplicative inverse of 2 is \[\dfrac{1}{2}\].5 days ago

https://www.vedantu.com › the-sum...

The sum of additive inverse and multiplicative inverse of 2 is ______.(a). \\[\\dfrac{3}{2}\\](b). \\[\\dfrac - Vedantu

There are 7 desserts that have both yogurt and fruit. Therefore, the answer to your question is 7.

To find out how many of the desserts with yogurt also include fruit, we need to use the concept of intersection in set theory. We can create two sets: one for desserts with yogurt and another for desserts with fruit.

The set of desserts with yogurt has 8 elements, and the set of desserts with fruit has 7 elements. We can represent these sets as follows:

Y = {yogurt desserts} = {1, 2, 3, 4, 5, 6, 7, 8}
F = {fruit desserts} = {1, 2, 3, 4, 5, 6, 7}

Now we need to find the intersection of these sets, i.e., the desserts that have both yogurt and fruit. To do this, we can count the number of elements in the set Y ∩ F:

Y ∩ F = {yogurt and fruit desserts} = {1, 2, 3, 4, 5, 6, 7}

So there are 7 desserts that have both yogurt and fruit. Therefore, the answer to your question is 7.

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The questions for grade 7 math worksheets are typically prepared by math teachers, curriculum specialists, and educational publishers.

These professionals use their knowledge of math concepts and pedagogy to create questions that are appropriate for the grade level and aligned with educational standards.

Additionally, they may use feedback from students and other teachers to refine the questions and ensure they are effective for teaching and learning. It is important for the questions to be clear, accurate, and challenging in order to help students develop their math skills and prepare for more advanced concepts.

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The factorization of the polynomial x² - 4x + 3 are (x - 1)(x - 3)

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

x² - 4x + 3

Also, we have the graph

From the graph, we can see that the graph intersects the x-axis ar

x = 1 and 3

This means that the factors are

(x - 1) * (x - 3)

So, we have

(x - 1)(x - 3)

Hence, the factorization of x² - 4x + 3 are (x - 1)(x - 3)

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Solution:

Given:

The sketch of triangle ABC can be shown below;

Let M be the midpoint of line segment AC.

To get the length of the base AC;

Using the distance between two points formula;

Therefore, the length of the base is 5.099 units.

Part B:

To get the height of the triangle ABC, the height is BM from the sketch.

Hence, the coordinate of point M is needed.

To get point M which is the midpoint of the line segment AC, we use the formula to get the midpoint.

Hence, the height BM of the triangle is the distance between points B and M.

Using the distance between two points formula;

Therefore, the height of the triangle ABC is 1.581 units

We are given the population of a city in 2014 as 119,000 and the observed doubling time for the population as 17 years. We are asked to find an exponential model \(\( n(t) \)\) that represents the population growth.

To find an exponential model \(\( n(t) \)\) for the population growth, we can use the general form of an exponential function, which is \(\( n(t) = n_0 \times e^{kt} \)\), where \(\( n_0 \)\) represents the initial population, \(\( t \)\) represents the time, \(\( e \)\) is the base of the natural logarithm, and \(\( k \)\) is the growth rate.

Given that the population in 2014 is 119,000, we have \(\( n_0 = 119,000 \)\). We are also told that the population doubles in 17 years. This means that the population after 17 years will be twice the initial population. So, we can write the equation:

\(\( 2 \times n_0 = n_0 \times e^{17k} \)\)

Simplifying, we get:

\(\( 2 = e^{17k} \)\)

To solve for \(\( k \)\), we take the natural logarithm of both sides:

\(\( \ln(2) = 17k \)\)

Finally, we can solve for \(\( k \)\) by dividing both sides by 17:

\(\( k = \frac{\ln(2)}{17} \)\)

Substituting the value of \(\( k \)\) in the exponential model equation, we get the exponential model \(\( n(t) = 119,000 \times e^{\frac{\ln(2)}{17}t} \)\). This equation represents the population growth of the city over time.

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Answer:

50sq cm

Step-by-step explanation:

You have to divide the shape into two rectangles. You get a 4x8 and a 3x6.

So then you have 32sq sm and 18sq cm. Add them up and you get 50sq cm.

The total number of points scored by the other 7 team members in Euclid high school's last basketball game is 11.

For the given question.

Let 't' be the total points scored.

Alexa = 1/4 t.

Brittany = 2/7 t

Chelsea = 15

Let 'x' be the points scored by remaining 7 team.

Thus, the two variable equation becomes.

1/4 t +  2/7 t + 15 + x = t   .....eq 1

Where, x ≤ 14 ( for 7 terams)

Simplifying eq 1.

15 + x = 13/ 28 t

28x + 28 = 13 t

Now, t must be divisible by 28.

Let t = 28 u, u ≥ 0 and divisible by 28.

Thus,

x + 15 = 13u.

Then, u = 2( t = 56) has been the only candidates for which x = 11.

Thus, the total number of points scored by the other 7 team members is 11.

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Answer:

10724.29

Step-by-step explanation:

mean means average

so to find an average you add everything together then divide it by the amount of variables

m = (10150 + 10211 + 10424 + 10769 + 10884 + 11155 + 11477)/7

m = 75070/7

m = 10724.2857143

m = 10724.29

Answer:

-5

Step-by-step explanation:

-9+x = -14

Add 9 to each side

-9+x+9 = -14+9

x = -5

Answer:

-5

Step-by-step explanation:

You could figure out the answer by adding 9 to -14.

-14 + 9 = -5.

Step-by-step explanation:

they are the same because FIGH just the ENLARGEMENT of ABCD

Your monthly payment for the 60-month, 5.54% APR motorcycle loan to purchase your dream Harley-Davidson will be $136.88.

To calculate the monthly payment for a motorcycle loan, we can use the formula for the present value of an annuity. The formula is:

PMT = PV * r / (1 - (1 + r)^(-n))

Where:
PMT = Monthly payment
PV = Present value of the loan
r = Monthly interest rate
n = Number of months

In this case, the present value of the loan (PV) is $7,200, the monthly interest rate (r) is 5.54% divided by 12 (0.0554 / 12), and the number of months (n) is 60.

Plugging in these values into the formula, we get:

PMT = 7200 * (0.0554 / 12) / (1 - (1 + (0.0554 / 12))^(-60))

Evaluating this expression, the monthly payment comes out to be approximately $136.88.

Therefore, your monthly payment for the 60-month, 5.54% APR motorcycle loan to purchase your dream Harley-Davidson will be $136.88.

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Answer:

213 r8

Step-by-step explanation:

Answer:

213 remainder 8

Step-by-step explanation:

213*15=3195+8=3203

The best answer regarding the effects of carbon monoxide is option c, CO results in less oxygen loading hemoglobin but unloading is not changed.

Carbon monoxide binds up more tightly to the hemoglobin as compared to the oxygen molecules. This reduces the oxygen-carrying capacity of the blood and results in less oxygen loading onto hemoglobin.

However, once oxygen is already bound to hemoglobin, CO does not significantly affect its release or unloading. Therefore, option c is the most accurate statement among the given choices.

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Answer:

It is A

Step-by-step explanation:

Because the arrow is pointing behind 4.4

Hope this helps:)

We then applied the formula for factoring perfect square trinomials to obtain the fully factored form, which is 4(2x - 3)2.

To factor 16x2 - 48x + 36 completely, we can first factor out the greatest common factor of 4:

16x2 - 48x + 36 = 4(4x2 - 12x + 9)

Now,

we can see that the expression inside the parentheses is a perfect square trinomial, which can be factored as:

4x2 - 12x + 9 = (2x - 3)2

Therefore, putting the pieces together, we have:

16x2 - 48x + 36 = 4(4x2 - 12x + 9) = 4(2x - 3)2

Hence, the fully factored form of the given expression is 4(2x - 3)2, which is option D).

The reason why we can recognize 4x2 - 12x + 9 as a perfect square trinomial is because it has the form a2 - 2ab + b2, where a = 2x and b = 3. This form can always be factored as (a - b)2, which in this case gives (2x - 3)2. The factor of 4 in the final answer comes from the fact that we initially factored out a 4 from the given expression.

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Answer:

7(n+8)

Step-by-step explanation:

It says 7 times the SUM of a number, n, and 8. According to the order of operations or PEMDAS, you would find the sum first, which would be in parenthesis, and then multiply by the 7.

Hope this helps! :)

Answer:

13 degrees

Step-by-step explanation:

Let x be the degree measure of the angle's complement

Then we have the other angle is x + 64

Because the 2 angles complement each other so the sum of the 2 angles is 90

So we have the equation: 2x + 64 = 90

<=> 2x = 26

<=> x = 13

a. The missing probability value is 0.4.

b. E(X) = 1.4.

c. Var(X) = 0.56 and σx = 0.75.

d. E(Z) = 2.27, Var(Z) = 2.56, and σz = 1.60.

The given probability distribution of the random variable X shows the probabilities associated with each possible outcome. To find the missing probability value, we know that the sum of all probabilities must equal 1. Therefore, the missing probability can be calculated by subtracting the sum of the probabilities already given from 1. In this case, 0.1 + 0.2 + 0.3 = 0.6, so the missing probability value is 1 - 0.6 = 0.4.

To find the expected value or mean of X (E(X)), we multiply each value of X by its corresponding probability and then sum up the results. In this case, (0 * 0.1) + (1 * 0.2) + (2 * 0.3) + (3 * 0.4) = 0.4 + 0.2 + 0.6 + 1.2 = 1.4.

To calculate the variance (Var(X)) of X, we use the formula: Var(X) = Σ[(X - E(X))^2 * P(X)], where Σ denotes the sum over all values of X. The standard deviation (σx) is the square root of the variance. Using this formula, we find Var(X) = [(0 - 1.4)² * 0.1] + [(1 - 1.4)^2 * 0.2] + [(2 - 1.4)² * 0.3] + [(3 - 1.4)² * 0.4] = 0.56. Taking the square root, we get σx = √(0.56) ≈ 0.75.

Now, let's consider the new random variable Z = 1 + (2/3)X. To find E(Z), we substitute the values of X into the formula and calculate the expected value. E(Z) = 1 + (2/3)E(X) = 1 + (2/3) * 1.4 = 2.27.

To calculate Var(Z), we use the formula Var(Z) = (2/3)² * Var(X). Substituting the known values, Var(Z) = (2/3)² * 0.56 = 2.56.

Finally, the standard deviation of Z (σz) is the square root of Var(Z). Therefore, σz = √(2.56) = 1.60.

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Answer:

12000

Step-by-step explanation:

sqrt144*1000000= sqrt144*sqrt10^6= 12*10^3=12000

Answer:

(-12x - 25) / (x + 3) (x - 5)

Step-by-step explanation:

1 - 2x/(x+3) + (x+3)/(x - 5)

= {(x + 3)(x - 5) - 2x(x - 5) + (x + 3)(x - 3)} / (x + 3) (x - 5)

= {(x² -5x + 3x - 16) - (2x² + 10x) + (x² - 3x + 3x - 9)} / (x + 3) (x - 5)

= x² - 2x - 16 - 2x² - 10x + x² - 9 / (x + 3) (x - 5)

= x² - 2x² + x² - 2x - 10x - 16 - 9 / (x + 3) (x - 5)

= (-12x - 25) / (x + 3) (x - 5)

Answer:

The correct option is third, H = - 14

Step-by-step explanation:

H = - 2×7

= -14

A tip of 18% was given to the restaurant after the meal and tax to the nearest percentage.

Cost of the food = $25.30

Tax on the food cost = 8%

Tax amount

= 8% of 25.30

= 0.08  × 25.30

= 2.204

Total cost of food before tip = 25.30 + 2.204 = $27.504

Tip given = 32.24 - 27.504 = 5.036

Tip percentage

= 5.036 / 27.504 × 100%

= 18.31%

≈ 18%

Hence a tip of 18% was given to the restaurant after the meal and tax to the nearest percentage.

Percentage increases and decreases are calculated by computing the difference between two numbers or by comparing that difference to the starting value.

One can calculate how significantly the initial value has changed mathematically by dividing the result by the starting value and using the absolute value of the difference between the two values.

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The total distance traveled in the first 3 seconds is 53/6 meters.

If a particle is moving at constant velocity, then its acceleration is zero. We can find the acceleration by taking the second derivative of the position function s(t):

s(t) = t³ - 6t² + 9t + 4

s'(t) = 3t² - 12t + 9

s''(t) = 6t - 12

Setting s''(t) = 0, we get:

6t - 12 = 0

t = 2

Therefore, when t = 2, the particle is moving at constant velocity. We can find the position s(2) by plugging in t = 2 into the position function:

s(2) = 2³ - 6(2)² + 9(2) + 4 = 12

So the position of the particle when it is moving at constant velocity is s = 12.

To find the total distance traveled in the first 3 seconds, we need to integrate the absolute value of the velocity function v(t) over the interval [0, 3]. We can find the velocity by taking the derivative of the position function s(t):

s(t) = t⁴ - 6t³ + 12t² - 10t + 3

v(t) = s'(t) = 4t³ - 18t² + 24t - 10

The absolute value of v(t) is |v(t)| = v(t) when v(t) ≥ 0, and |v(t)| = -v(t) when v(t) < 0. We can split the integral into two parts, one where v(t) is non-negative and one where v(t) is negative:

s(3) - s(0) = ∫₀³ |v(t)| dt

= ∫₀² v(t) dt - ∫₂³ v(t) dt

Evaluating the integrals:

= [t⁴/4 - 6t³/3 + 12t²/2 - 10t]₀² - [t⁴/4 - 6t³/3 + 12t²/2 - 10t]₂³

= (16/3 - 27/2 + 36 - 10) - (-8/3 + 27/2 - 27 + 10)

= 14/3 + 9/2 + 10

= 53/6m

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Answer:

B,C,E

Step-by-step explanation:

khan academy

Side length of the scaled copy of square is smaller than original.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given,

Scale factor of scaled copy of square is less than 1.

Scale factor basically defines the ratio between the sides of the constructed square to that of the original square.

if scale factor is less than 1 then the sides of the constructed square is smaller than that of the original square.

Hence, side length of constructed square is smaller than the original square.

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Given :-

To Find :-

Solution :-

Here we are given that ,

\( f(x) = 2x + 5 \)

Substituting x = a , we have ,

\( f(a) = 2a + 5\)

Now f(a) = 20 . So ,

\(20 = 2a + 5 \)

Solve out for a ,

\( 20 - 5 = 2a\\\)

\( 2a = 15\\\)

\( a = \dfrac{15}{2}= 7.5\)

Hence the value of a is 7.5

For finding out the value of b , substitute x = b , and f(b) = 0 ,

\( f(b) = 2b + 5 \\\)

\(0 = 2b + 5 \)

Solve for b ,

\( 2b = -5 \\\)

\( b =\dfrac{-5}{2}=-2.5\)

Hence the value of b is -2.5

4th option is correct .

I hope this helps.

Answer:  choice (4)

a = 7.5 and b = -2.5

=======================================

Work Shown:

f(x) = 2x+5

f(a) = 2a+5  .... replace every x with 'a'

20 = 2a+5 .... replace f(a) with 20, since f(a) = 20

2a+5 = 20

2a = 20-5 .... subtract 5 from both sides

2a = 15

a = 15/2 ... dividing both sides by 2

a = 7.5

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

f(x) = 2x+5

f(b) = 2b+5 ... replace every x with b

0 = 2b+5 .... replace f(b) with 0, since f(b) = 0

2b+5 = 0

2b = -5 .... subtract 5 from both sides

b = -5/2 .... divide both sides by 2

b = -2.5

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

We have a = 7.5 and b = -2.5. So we go for choice (4)

Outfitters must sell at least 0.4 shirts, which is approximately equal to 0 shirts, to break even.

An equation is a mathematical statement that states that two expressions are equal. It usually consists of variables, coefficients, and constants, connected by operations such as addition, subtraction, multiplication, and division. Equations are used to model relationships between different quantities and to solve problems in various fields such as physics, engineering, and economics. For example, the equation y = mx + b represents a straight line in two-dimensional space, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

Let's define the variables:

x = the number of shirts Outfitters must sell to break even

c = the total cost of production (plain gray T-shirt + screen printing) = $3.50 + $2.50 = $6.00

p = the selling price of the T-shirt = $15.00

The equation to represent the number of shirts Outfitters must sell to break even can be written as follows:

x * p = x * c

Solving for x:

x = c / p

x = $6.00 / $15.00

x = 0.4

Outfitters must sell at least 0.4 shirts, which is approximately equal to 0 shirts, to break even. However, since they can't sell fractional shirts, they must sell at least 1 shirt to break even.

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