1. Kim ran the 100-meter race in 135.46 seconds. Tyron ran faster by 15.7 seconds. What was Tyron’s time for the 100-meter dash?

2. Janna takes her medicine 3 times a day. How many days will a 60 ml medicine last if ml is taken each time?

3. May bought 23 of a kilo of meat. She cooked 12 of it. How much did she cook?

4. Arjay bought 8.75 meters of cloth for ₱813.75. Find the cost price per meter.

5. Jay will divide his P112,000 among his 3 brothers. His elder brother will receive of the amount while the remaining amount is to be equally divided among the two younger brother. How much will each of the younger brothers receive?

The initial value  of the function f(x) = 3x + 7 is 7

The function is given as:

f(x) = 3x + 7

The above function is a linear function

A linear function is represented as

f(x) = mx + c

Where c represents the initial value

By comparing the equations f(x) = 3x + 7 and f(x) = mx + c, we have:

c = 7

This means that the initial value  of the function f(x) = 3x + 7 is 7

Hence, the initial value  of the function f(x) = 3x + 7 is 7

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Complete question

Identify the initial value for the function f(x) = 3x + 7?

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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The answer choice which correctly draws a comparison between the end behaviors of the functions is; Choice C; They have the same end behavior as x approaches -∞ and same end behavior as x approaches ∞.

As given in the task content; the graph of the exponential function passes through (-4, 9), (0, 1), (1, 0), and (5, -2).

It therefore follows that as; x reduces (approaches -∞), the y value increases.

And, as x -increases (approaches +∞), the y-value decreases.

For the table, the values can be written as coordinates as follows; (-1,2), (0,4), (1,6), (2, 0), (3,-2).

Consequently, as x reduces (approaches -∞), the y- values decrease.

And, as x increases (approaches +∞), the y-values decrease.

Ultimately, the two functions in discuss can be concluded to have; Choice C.

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The  number of 50¢ coins is 200, number of  25¢ coins is 360

and number of  10¢ coins is 160.

The quantitative relation between two or more amounts showing the number of times one value is contains or contained within other.

Now the given ratio is 5 : 9 : 4.

and total amount of the coins is $206.

There are three types of coins in the bag, 50¢, 25¢ and 10¢.

Suppose x be the the ratio of coins in the bag.

Hence, number of  50¢ coins = 5x

number of  25¢ coins = 9x

number of  10¢ coins = 4x

Now, given total amount = $206

and since $1 = 100¢

⇒ ($0.5)(5x) + ($0.25)(9x) + ($0.1)(4x) ¢ = $206

Solving them,

⇒ 2.5x + 2.25x + 0.4x = 206

⇒ 5.15x = 206

⇒ x = 40

Therefore,

number of  50¢ coins = 5*40 = 200

number of  25¢ coins = 9*40 =  360

number of  10¢ coins = 4*40 =  160

Hence, number of 50¢ coins is 200, number of  25¢ coins is 360

and number of  10¢ coins is 160.

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Answer: 10

Step-by-step explanation: The common denominator for these two

fractions is simply the least common multiple for the two denominators.

Since our denominators of 5 and 2 have no factors in common,

our least common denominator is 5 · 2 or 10.

The trade this country will import is given by the option (C) 300 pair of shoes.

The number of shoes exported will be calculated by the formula -

Import = quantity demanded - quantity supplied. The formula is based on the concept that the import of shoes will be carried out once the manufacturing is more than the demand.

The graph indicates the quantity demanded is 1000 and the quantity supplied is 1300. Keep the values in formula to find imports.

Imports = 1300 - 1000

Performing subtraction on Right Hand Side of the equation

Imports = 300

Hence, the import is 300.

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The complete question is attached in figure.

Answer:

15

Step-by-step explanation:

1+3+5+4+2

Given:

The polynomial function is

\(q(x)=6x^3+19x^2-15x-28\)

Yuri thinks that \(\dfrac{3}{4}\) is a root of the given function.

To find:

Why \(\dfrac{3}{4}\) cannot be a root?

Solution:

We have,

\(q(x)=6x^3+19x^2-15x-28\)

If \(\dfrac{3}{4}\) is a root, then the value of the function at \(\dfrac{3}{4}\) is 0.

Putting \(x=\dfrac{3}{4}\) in the given function, we get

\(q(\dfrac{3}{4})=6(\dfrac{3}{4})^3+19(\dfrac{3}{4})^2-15(\dfrac{3}{4})-28\)

\(q(\dfrac{3}{4})=6(\dfrac{27}{64})+19(\dfrac{9}{16})-\dfrac{45}{4}-28\)

\(q(\dfrac{3}{4})=3(\dfrac{27}{32})+\dfrac{171}{16}-\dfrac{45}{4}-28\)

\(q(\dfrac{3}{4})=\dfrac{81}{32}+\dfrac{171}{16}-\dfrac{45}{4}-28\)

Taking LCM, we get

\(q(\dfrac{3}{4})=\dfrac{81+342-360-896}{32}\)

\(q(\dfrac{3}{4})=\dfrac{-833}{32}\neq 0\)

Since the value of the function at \(\dfrac{3}{4}\) is not equal to 0, therefore, \(\dfrac{3}{4}\) is not a root of the given function.

Answer: B

Step-by-step explanation:

To find out how far the turtle went in 16 seconds you have to multiply 16 and -8

Answer:

I have the same question on test and answer is B

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

3/4 x - 3 = -18

You should try to get all of one term on one side of the equation, and have the constant on the other side so the next step would be easy.

Here are the steps after you add 3:

3/4 x = -15

x = -5/4 (divide by 3/4 on both sides)

Answer is in the screenshot:

Answer:

761.25 m³

Step-by-step explanation:

l = 15 , w = 14.5 , h = 3.5

Volume of a rectangular prism is given by the formula :

V = lwh

V = 15 × 14.5 × 3.5

V = 761.25

Units will be m³

I am attaching an image for visual understanding

Hope this helped and brainliest please.

SOLUTION

Given the question in the image, the following are the solution steps to answer the question

STEP 1: Write the daily routes for the first 8 days

STEP 2: Compute the arithmetic mean for the first 8 days

The mean of the distances of these 8 days is 83.25km

STEP 3: Compute the median of the distances of these 8 days

To find the Median, place the numbers in ascending order and find the middle number.

The median of the distances of these 8 days is 85km

STEP 4: Calculate the average distance needed in order to reach her goal

Therefore, the average distance needed in the remaining days in order to reach her goal is 76.75km

The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.

The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.

The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.

The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).

Based on this information, we can draw the following conclusions:

The graph will be a U-shaped curve with the vertex at (1, -9).

The vertex represents the minimum point of the parabola since it opens upward.

The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.

The graph will extend indefinitely in both directions.

To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.

Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.

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After making payments for 15 years, the amount still owed on the mortgage would be approximately $145052.36.

To determine how much will still be owed after making payments for 15 years, we can use the formula for the remaining balance on a mortgage:

Remaining balance = P ((1 + r)ⁿ - (1 + r)ᵇ) / ((1 + r)ⁿ - 1)

where:

P = the initial loan amount (in this case, $219,000)

r = the monthly interest rate (which is the annual interest rate divided by 12)

n = the total number of monthly payments (which is 30 years times 12 months per year, or 360 months)

b = the number of monthly payments made so far (which is 15 years times 12 months per year, or 180 months)

First, we need to calculate the monthly interest rate:

r = 4.5% / 12 = 0.00375 = 0.375%

Next, we can plug in the values to get:

Remaining balance = $219,000 ((1 + 0.00375)³⁶⁰- (1 + 0.00375)¹⁸⁰) / ((1 + 0.00375)³⁶⁰ - 1)

= $145052.36

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The linear equation for the cost of lemonades is 1.50*x+6 where x=5 i.e. A   and he spends $54.75 in total.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Cost of lemonade=$1.5, number of lemonades=5

Cost of hamburger=$8.25, number of hamburgers=5

Tip=$6

Hence,

        Total cost=5*1.5+5*8.25+6

          Total cost =$54.75

Cost of lemonades only = 5*1.5+6

In type of linear equation  1.50*x+6 where x=5

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Answer:

38

Step-by-step explanation:

Notice that the first triangle is an isosceles triangle, meaning that the base angles are equivalent. Since one angle is 62, we know that the other is 62 as well, which makes 124. This means that angle 2 is 56 degrees. Since 2 and 3 are on the same 'line', they both add up to 180. If 2 is 56, then angle 3 is 124. So the three angles inside the triangle are 124, 18, and x. So, 124+18=142. 180-142= 38

The distance from the floor when t = 6.5 seconds is about 13.7 cm.

We are given that;

H(t)=A cos (Bt) +D

Now,

b. To write an equation of the form H(t) = A cos (Bt) + D for the graph, we need to find the values of A, B, and D.

A is the amplitude of the cosine function, which is half the difference between the maximum and minimum values of H(t). In this case, the maximum value is 36 and the minimum value is 12, so:

A = (36 - 12) / 2 A = 12

D is the vertical shift of the cosine function, which is the average of the maximum and minimum values of H(t). In this case:

D = (36 + 12) / 2 D = 24

B is related to the period of the cosine function, which is the time it takes for one complete cycle. In this case, the period is 8 seconds, because H(t) repeats its values every 8 seconds. The formula for B is:

B = 2π / period

So:

B = 2π / 8 B = π / 4

Therefore, the equation is:

H(t) = 12 cos (π/4 t) + 24

c. To find the distance from the floor when t = 6.5 seconds, we need to plug in t = 6.5 into the equation and evaluate H(t). Using a calculator, we get:

H(6.5) = 12 cos (π/4 × 6.5) + 24 H(6.5) ≈ 13.7

Therefore, by the equation answer will be 13.7 cm.

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Answer:

\( \frac{67}{30} \: \text{or} \:2 \frac{7}{30} \)

Step-by-step explanation:

5/6 ÷ 1/3 - 2/3 (2/5)

Hope it helps you! ＼(^ᴥ^)／

Answer: y = -9/8 + 7

Step-by-step explanation:

point a = (0,7), point b = (8,-2)

y = mx + b

b = 7

y = mx + 7

-2 = 8m + 7

-9 = 8m

m = -9/8

y = -9/8 + 7

Answer:

y= -9/8x+7

Step-by-step explanation:

find the slope

y2-y1/x2-x1

-2-7/8-0

-9/8

y=mx+b

m=slope

b=y intercept

y=  - 9/8x + b

y= -9/8x+7

9514 1404 393

Answer:

  \(\displaystyle S_n=\sum_{k=1}^n{4(-3)^{k-1}}\)

Step-by-step explanation:

The first term of this geometric series is 4. The common ratio is -12/4 = -3, so the general term is ...

  an = 4·(-3)^(n-1)

The sum is the sum of terms of this form.

  \(\displaystyle S_n=\sum_{k=1}^n{4(-3)^{k-1}}\)

Answer:

6/8

Step-by-step explanation:

Answer:

30m

Step-by-step explanation:

A=πr²

225π=πr²

225=r²

r=√225

r=15

d=2r

d=2×15

=30m

a. Let \(d\) be the number of daytime calls Eshwa makes, and \(e\) the number of evening calls. Then the cost \(C\) (in pence) of making \(d+e\) calls is

\(C = \boxed{50d + 40e}\)

b. £1 = 100p, so the cost \(C'\) (in £) is 1/100 of the cost found in part (a),

\(C' = \dfrac{50d + 40e}{100} = \boxed{\dfrac d2 + \dfrac{2e}5}\)

c. If Eshwa makes 30 of each type of call in a month, then the total cost (in £) is

\(C' = \dfrac{30}2 + \dfrac{2\cdot30}5 = \boxed{27}\)

c2. If Eshwa makes 20 daytime calls and 50 evening calls, then the total cost (in £) is

\(C' = \dfrac{20}2 + \dfrac{2\cdot50}5 = \boxed{30}\)

d. Let \(e=40\) and \(C'=42\). Solve for \(d\).

\(42 = \dfrac d2 + \dfrac{2\cdot40}5\)

\(42 = \dfrac d2 + 16\)

\(\dfrac d2 = 26\)

\(d = \boxed{52}\)

The total time for the trip is:

T =  3mi*( 3/2x).

Where x is the rate at which she comes home.

Remember the relation:

distance = rate*time.

We know that the distance is 3 miles (done twice).

First, the rate is 2x and then the rate is x, then the time it took the first half is:

t = 3mi/2x

And for the coming back:

t = 3mi/x

Then the total time for the trip is:

T =  3mi/2x +  3mi/x = 3mi( 1/2x + 1/x) = 3mi*( 3/2x).

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To solve this problem, we need to use Charles's law, which states that, at constant pressure, the volume of a sample of gas is directly proportional to its temperature.

The law can be expressed mathematically as:

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{ \frac{V_1}{T_1}=\frac{V_2}{T_2} } \end{gathered}$} }\)

Where:

Now we obtain the data to continue solving:

Now, we will convert the temperatures to Kelvin:

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_1=220 \ ^{\circ}C+273=493 \ Kelvin} \end{gathered}$} }\)

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_2=40 \ ^{\circ}C+273= 313 \ Kelvin} \end{gathered}$} }\)

Now we solve for V₂:

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{V_1T_2}{T_1 } } \end{gathered}$} }\)

Where:

Now, we substitute the values in the formula:

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{(0.5 \ L\times313\not{k} )}{493\not{k} } } \end{gathered}$} }\)

\(\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2\approx0.32 \ Liters } \end{gathered}$} }}\)

Answer:

Step-by-step explanation:

3³ × 4³ = (3×4)³ = 12³

:::::

3⁴ × 3³ = 3⁴⁺³ = 3⁷

:::::

3⁴ × 4³ = 3 × 3³ × 4³ = 3 × (3³ × 4³) = 3 × 12³ < 12¹²

Answer:

this is the final answer

thankyou

Step-by-step explanation:

V=lwh

3

The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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