During a basketball game, Kevin made a total of 14 shots. Each basketball shot is worth either 2 points or 3 points. Kevin scored a total of 34 points. Let a represent the number of 2 point shots and let y represent the number of 3 point shots.

Answer:

When multiplying exponents of the same base, add the exponents. When dividing exponents of the same base, subtract the exponents. When raising a power to a power, multiply the powers.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

For every 1 liter of water, 0.07 kilograms of salt must be added. They are asking for 0.5 liters of water, which is half of 1 liter. So therefore, they need half of 0.07 kilograms of salt, which is 0.035 kilograms

Answer:

0.035 kg.

Step-by-step explanation:

0.5 liter is 1/2 liter

0.07kilograms / 2 = 0.035kg

Answer:

hen he deposited some more money and his account balance was $28.

Step-by-step explanation:

Answer:7

Step-by-step explanation:

Answer:

4 2/3

Step-by-step explanation:

When dividing fractions you multiply the recipricol of the second term by the first.

1/3 x 5/1 = 5/3.

2 x 1 = 3

5/3 = 1 2/3

3 + 1 2/3 = 4 2/3.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

The simplest form of the resultant fraction when 2 1/3 divided 1 1/5

is 1 17/18.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given are two fractions 2 1/3 divided by 1 1/5.

We know,

2 1/3.

= (2×3 + 1)/3.

= 7/3 and similarly 1 1/5 is 6/6.

So, 7/3 divided by 6/5.

= (7/3)/(6/5).

= (7/3)×(5/6).

= 35/18.

= 1 17/18.

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Based on the fact that Kamama wants her hexagons to be congruent, the transformations that she can use are:

In order to have congruent shapes, there are three transformations that can be used.

Firstly, it is important to note that congruent shapes have the same size and the same shape. They are identical except for their orientation which may be different.

A reflection would create a congruent shape that would have the same size and angles but the orientation should be different. This is the same as a rotation. A translation will often result in congruent shapes that also have the same orientation. This means that Kanama can use any of these transformations.

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According to the given statement the interest that we earn is

=  $74,059 . 64

The present value of an annuity seems to be the current worth of future annuity payments based on a predetermined rate of return, as well as discount rate. The higher the discount rate, the smaller the annuity's present value.

monthly payment is 150

at the age = 30

interest rate = 4

till age of = 65

At age 65, the annuity would be worth $137,059.64.

We only need to determine the amount of interest. = ?

 for monthly payments, we need to take n, which equals 12 points now total interest. determined by future value. Substitute minus p m t multiplied by n multiplied by t for all values now.

the amount of interest   =  deposited amount x year x no of year invested

                                       = 150 x 12x(65-30)

           present value     = 63000

At age 65, the annuity would be worth $137,059.64.

We know that the interest is  = balance - capital

                                                 = 137,059.64 - 63000

                                                 = $74,059 . 64

According to the given statement the interest that we earn is

=  $74,059 . 64

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Answer:

A and C

Step-by-step explanation:

First because "AAS" is when we know two angles and one side (which is not between the angles). To solve an AAS triangle. use the three angles add to 180° to find the other angle. then The Law of Sines to find each of the other two sides.

And then C because all angles have to equal to the other angle pattern

Answer:

No, it isn't.

Step-by-step explanation:

The point on y = 5 should be on y = 7, and the point on x = 5 should be on x = 7. The attachment shown is what the graph should look like.

Answer:

[tex]x = \frac{9}{14} [/tex]

Step-by-step explanation:

6 (5x - 7) = -3 (4x + 7) + 6

30x - 42 = -12x - 21 + 6

30x - 42 = -12x - 15

30x + 12x = -15 + 42

42x = 27 ÷ 42

x = 27/42

simplify with factor 3

[tex]x = \frac{9}{14} [/tex]

Answer:

$0.98

Step-by-step explanation:

First, add $8.75 & $4.35.

8.75 + 4.35 = $13.10 in total

Then find the tax by multiply 7.5% (3/40) times 13.10.

3/40 * 131/10

393/400 = 0.9825, which rounds down to $0.98 in tax

Answer:

Step-by-step explanation:The largest fraction is 5/8

The set of actors with at least a return of $7.50 are {H, J, K}

The actors that would be included in this set include actors that earn an amount equal to $7.50 or an amount greater than $7.50.

A set can be described as a collection of objects whose elements are fixed and cannot be changed. Thus, elements in this set would include those who earn more than or equal to $7.50.

To write a set in a roster form, the elements in the set are written in a row within curly brackets or braces - { }. The elements in the set are then separated by commas.

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Answer:

a number question's answer is a power 2. and is c power 1

Answer:

410.941

Step-by-step explanation:

Answer: 3x + 15

Step-by-step explanation:

In order to use the distributive property, you simply multiply the number on the outside by both the number inside the parenthesis

So, in this case, we would multiply 3 by X and 3 by 5

3 times x = 3x

3 times 5 =15

Your new equation is then made by adding these two together

3x+15

Answer 3x + 15

Answer:I’m pretty sure I got this one right too

Step-by-step explanation:

The actual speed of the airplane is 472.56 mph in the direction of 41.57° north of west.

"In a two-dimensional coordinate system, any vector can be broken into x -component and y -component according to axis."

We can assume, east as the positive x- axis and north as the positive y-axis, respectively.

Similarly, west as the negative x- and south as the negative y-axis, respectively.

Therefore, the x- and y-components of the speeds.

Now, for the airplane:

x-component: - 500 × cos(45°) mph = - 353.55 mph

y-component: 500 × sin(45°) mph = 353.55 mph

For the wind:

y-component: -40 mph

Therefore, sum of the x-components = -353.55 mph

Similarly, sum of the y-components = (353.55 - 40) mph = 313.55 mph

Now, the actual speed =

[tex]\sqrt{(-353.55)^{2} + (313.55)^{2}}[/tex] mph

= [tex]\sqrt{223313.6}[/tex] mph

= 472.56 mph

Now, the direction of the airplane is:

tan(Ф) = [tex]\frac{313.55}{- 353.55}[/tex]

⇒ Ф = tan⁻¹( [tex]\frac{313.55}{- 353.55}[/tex])

⇒ Ф = - 41.57°

The actual speed of the airplane is 472.56 mph in the direction of 41.57° north of west.

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Answer:

thank for the free point

Answer: (-3,1)

Step-by-step explanation:

inputting the two equations into a graphing calculator tells us that these two lines intersect at the point (-3,1)

Answer:

7.77%

Step-by-step explanation:

When dealing with calculating a sequence of probabilities for an specific event such as this one you simply need to multiply the seperate probabilities of each part of the event happening together. Which in this case would be 21% and 37%. We first need to convert these percentages into decimal form by dividing each of them by 100. Once we have the decimal form we multiply them together to find the answer.

21% / 100 = 0.21

37% / 100 = 0.37

0.21 * 0.37 = 0.0777   ... multiply by 100 to get percent form

0.0777 * 100 = 7.77%

Finally, we can see that the probability that a first-year student requires both a developmental math course and a developmental English course is 7.77%

The probability that a first year student requires both a development math course and a developmental English course is 7.77%

Since The probability that a first year student entering a certain private college needs neither a developmental math course nor a developmental English is 61% while 21% require a developmental math course and 37% require a developmental English course.

So, the probability is

[tex]= 0.21 \times 0.37[/tex]

= 7.77%

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Answer:

[tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{e^\big{arctan(3e^{4x})}}{2} + C[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Integration

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx[/tex]

Step 2: Integrate Pt. 1

Step 3: integrate Pt. 2

Set variables for u-substitution.

Step 4: Integrate Pt. 3

Step 5: Integrate Pt. 4

Set variables for u-substitution #2.

Step 6: Integrate Pt. 5

Step 7: Integrate Pt. 6

Set variables for u-substitution #3.

See attachment for rest of work (would not fit entire answer in answering box).

Answer:

domain: [-4, ∞)

range: [-6, ∞)

Step-by-step explanation:

look at the graph. for domain, you want the x-values included in the interval. the endpoint at -4 means that the domain begins at -4. since the graph extends to positive infinity, then include that in domain with an parentheses not bracket since there's no endpoint.

for range, do the same thing but for y-values.

The domain and the range of a function are the possible x and y values it can take

The domain

From the graph, the x-value starts at x = -4, and it continues to the right.

The dot at x = -4, means that -4 is inclusive of the x values.

The arrow at the other end means that, the value increases to infinity.

So, the domain of the function is: [tex][-4, \infty)\\[/tex]

The range

From the graph, the y-value starts at y = -6, and the curve open upwards

The arrow at the other end means that, the value increases to infinity.

So, the range of the function is: [tex][-6,\infty)[/tex]

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The equation's line that is steeper is y = 3x + 7

From the question, we are to determine which of the given equations' line is steeper

The given equations are

y = 3x + 7

and

y = (1/2)x + 9

First, we will compare the equations to the form of an equation of a straight line

The equation of a straight line is of the form

y = mx + c

Where m is the slope

and c is the y intercept

Thus,

The slope of the equation, y = 3x + 7, is 3

and

The slope of the equation, y = (1/2)x + 9, is 1/2

NOTE: The higher the slope of a line, the steeper the line

Hence, the equation's line that is steeper is y = 3x + 7

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Answer:

9/2π cm/s

Step-by-step explanation:

Volume of the spherical balloon V= 4/3πr³

Rate of change of volume dV/dt = dV/dr * dr/dt

dV/dr = 3(4/3πr²)

dV/dr = 4πr²

dV/dr = 4π(2)²

dV/dr = 16π

If V = 72cm²/s

72 = 16π*dr/dt

dr/dt = 72/16π

dr/dt = 9/2π cm/s

Hence the radius is changing at  9/2π cm/s

Answer:

80 square units

Step-by-step explanation:

The figure given can be decomposed to have two trapezoids of equal dimensions and a rectangle.

Area of the figure = (2*area of a trapezoid) + (area of a rectangle)

Area of the 2 trapezoids:

Area of the two trapezoid = 2(½(a + b)*h)

Where,

a = 2 + 6 + 2 = 10 units

b = 6 units

h = 2 units

Plug in the values:

Area of the two trapezoid = 2(½(10 + 6)*2)

= 2(½(16)*2)

Area = 32 units²

Area of the rectangle:

Area = length × width

Length = 8 units

Width = 6 units

Area = 8 × 6 = 48 units²

✔️Area of the figure = 32 + 48 = 80 units²

Answer:

a) The negative sign indicates that progression is decreasing in time and decreases by 18 percent each month.

b) Antonio is expected to make a profit of 37445.17 in 7 months from now.

Step-by-step explanation:

a) The equation described on statement represents a geometrical progression, which is defined as:

[tex]y = C_{o}\cdot (1+ r)^{x}[/tex] (1)

Where:

[tex]C_{o}[/tex] - Initial amount, measured in monetary units.

[tex]r[/tex] - Rate, dimensionless. (The progression is increasing when [tex]r > 0[/tex], and decreasing when [tex]-1 < r < 0[/tex])

[tex]x[/tex] - Time, measured in months.

[tex]y[/tex] - Profit, measured in monetary units.

Given that [tex]y = 150,210\cdot (0.82)^{x}[/tex], we calculated the rate below:

[tex]1+r = 0.82[/tex]

[tex]r = 0.82-1[/tex]

[tex]r = -0.18[/tex]

The negative sign indicates that progression is decreasing in time and decreases by 18 percent each month.

b) If we know that [tex]x = 7[/tex], then the expected amount for Antonio in 7 months from now is:

[tex]y = 150,210\cdot (0.82)^{7}[/tex]

[tex]y = 37445.17[/tex]

Antonio is expected to make a profit of 37445.17 in 7 months from now.

Answer:

12

Step-by-step explanation:

Answer:

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