Marissa's mom purchased coffee from the local coffee shop. The first cup of coffee was $3.95. Each refill is $1.50. She also decided to get a bagel for $3.00. If Marissa's mom had 2 refills and a $0.50 discount as part of the rewards program, how much did she spend at the coffee shop?

$9.95
$9.45
$8.65
$7.95

Answer:

The number is 16.

Step-by-step explanation:

3x=32+x

2x=32

x=16

A number that when tripled, gives the same result as when 32 is added to it is 16.

In this exercise, you're required to solve for an unknown number, that when tripled has the same value as when 32 is added to it.

Translating the word problem into an algebraic expression, we have;

Tripling the number, we have:

\(3x\)    ....equation 1

Adding 32 to the number, we have:

\(32 + x\)   ....equation 2

Equating the two equations, we have:

\(3x = 32 + x\\\\3x - x = 32\\\\2x = 32\\\\x = \frac{32}{2}\)

x = 16

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Answer:

Step-by-step explanation:

number 6. (1-2+3)  - 4 + 5 = 3

Number 7. (1+2) +( 3+4 ) - 5 = 5

number 8. (1+2+3) - 4(5) = 10

5: (1+2)3 - 4 / 5 = 1

Answer:

5 --- 1 + 2 - 3 - 4 + 5 = 1

6 --- 1 - 2 + 3 - 4 + 5 = 3

7 --- [1 + (2 x 3 x 4)] / 5 = 5

8 --- [1 + 2 + (3 x 4)] - 5 = 10

Step-by-step explanation:

I didn't know if you needed brackets/parenthesis for the first two, that's just what I came up with

South Carolina can produce 26x26x10x10x10 = 676,000 different license plates with the configuration digit, letter, digit, letter, digit, digit.

Permutations are arrangements of objects in a specific order. For example, if you have the letters A, B, and C, the possible permutations are ABC, ACB, BAC, BCA, CAB, and CBA. Permutations are often used to calculate the total number of possible combinations for a given set of objects, as each permutation is a unique combination. For example, if you have three letters and three digits, the total number of permutations is 26x10x10x26x26x10 = 17576000.

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Each interior angle of a regular dodecagon measures 150 degrees.

To find the measure of each interior angle of a regular dodecagon, we can use the formula:

Interior angle = (n-2) x 180° / n

where n is the number of sides of the polygon.

For a regular dodecagon, n = 12. Plugging this into the formula, we get:

Interior angle = (12-2) x 180° / 12
Interior angle = 10 x 180° / 12
Interior angle = 150°

Therefore, each interior angle of a regular dodecagon measures 150 degrees.

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In a case whereby the slide part of a water slide is 89 feet long and makes a 42 angle of depression with the ground, the lenght or how high up in the air  is 73.6 feet

We know that the length of the slide AB is 89 feet, and the angle of depression from A to B is 42 degrees. We want to find the height h of point A above the ground.

The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is h (the height we're looking for), and the adjacent side is AB (the length of the slide). So we can write base on trigonometery as ;

tan(42) = h / 89

h = 89 * tan(42)

h ≈ 73.6 feet

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The value for g is 2, meaning that each family bowled 2 games.

How to solve linear equations?
Given that the largest power of the variable (or pronumeral) in these equations is 1, linear equations are also known as first-degree equations. A line on the quadratic system is represented by a linear equation. This equation's general form is axe + b = 0, where a, b, and x are all integers and x is the variable. The y-axis is parallel to this form of equation's single solution, which it symbolizes.
The steps that should be followed while solving linear equations are listed below:
1) We must first determine which variable we need to isolate.
2) Next, make a distinction between variables and constants.
3) Arrange the constants on the right and the variables on the left.
4) Using established axioms, we carry out algebraic operations to determine the variable's value.

Given, the equation is 6(8g + 2) + 45 = 153
Following the steps in the available literature, we have the equation as:
6(8g + 2) + 45 = 153 ⇒ 48g + 12 + 45 = 153 ⇒ 48g = 153 - 45 - 12 = 96
⇒ g = 96/48 ⇒ g = 2
Thus, g as suggested will determine number of times each family bowled.

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Thus, the given function shows the exponential decay with the decay rate of 3%.

A function having a variable exponent is said to be exponential.

Through an exponential function, the exponent serves as the independent variable, the x-value, and the base is a fixed value. A prime example of an exponential function is y = 2ˣ.

Given exponential function:

y= 21(0.97)ˣ

Exponential decay is represented by this equation. The function shows decay when such base is smaller than 1.

Formula for exponential decay is y = a(1-r)ˣ

In which, r - decay rate in decimal.

r = 1 - 0.97 = 0.03

r =  3%

Thus, the given function shows the exponential decay with the decay rate of 3%.

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Complete question:

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

y= 21(0.97)ˣ

Answer:

-5

Step-by-step explanation:

\(\boxed{slope = \frac{y1 - y2}{x1 - x2} }\)

*(x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate.

Slope of (1, 65) and (2, 60)

\( = \frac{65 - 60}{1 - 2} \\ = \frac{5}{ - 1} \\ = - 5\)

Answer:

I think the constraint of proportionality is 25 because each dot it increases buy 25.

I also believe that at 10 the total should be at 225.

Step-by-step explanation:

Let's find the rule in the pattern.

6, 4, 2, 0, -2.

To get to 4 you must subtract 2.

To get to 2 you must subtract 2.

To get to 0 you must subtract 2.

To get to -2 you must subtract 2.

The rule is to subtract 2.

Subtract 2 from -2 to represent the first unknown term.

\( - 2 - 2 = - 4\)

-4 is the next term.

Subtract 2 from -4 to represent the second unknown term.

\( - 4 - 2 = - 6\)

-6 is the next term.

Subtract 2 from -6 to represent the third unknown term.

\( - 6 - 2 = - 8\)

-8 is the next term.

To find the present value of $600 due in the future under each of the given conditions, we can use the formula for compound interest:

PV = FV / (1 + r/n)^(n*t)

Where:
PV = Present Value
FV = Future Value
r = Nominal interest rate
n = Number of compounding periods per year
t = Number of years

a. For a 9% nominal rate, semiannual compounding, and discounted back 9 years:
PV = 600 / (1 + 0.09/2)^(2*9)
  = 600 / (1 + 0.045)^(18)
  = 600 / (1.045)^(18)
  ≈ $275.55

b. For a 9% nominal rate, quarterly compounding, and discounted back 9 years:
PV = 600 / (1 + 0.09/4)^(4*9)
  = 600 / (1 + 0.0225)^(36)
  = 600 / (1.0225)^(36)
  ≈ $275.33

c. For a 9% nominal rate, monthly compounding, and discounted back 1 year:
PV = 600 / (1 + 0.09/12)^(12*1)
  = 600 / (1 + 0.0075)^(12)
  = 600 / (1.0075)^(12)
  ≈ $564.64

Please note that the values are rounded to the nearest cent as per the instructions.

Compound interest is a concept in finance and mathematics that refers to the interest earned or charged on both the initial amount of money (principal) and any accumulated interest from previous periods. It is a powerful concept that allows investments or loans to grow or accumulate faster over time.

The formula for compound interest can be expressed as:

A = P * (1 + r/n)^(nt)

Where:

A represents the future value or accumulated amount, including both the principal and interest.

P is the principal amount (initial investment or loan).

r is the annual interest rate (expressed as a decimal).

n is the number of compounding periods per year.

t is the number of years.

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\(y = \frac 14x^2\) is less steep than the parent quadratic equation, while \(y = 2x^2\) is steeper than the parent quadratic equation

The parent equation of a quadratic equation is represented as:

\(y = x^2\)

For a function to be steeper or less steep than the parent function must be stretched or compressed by a factor k

So, we have:

\(y = (kx)^2\)

If k is greater than 1, then the function would be steeper; else, the function would be less steep.

Assume k = 2, we have:

\(y = (2x)^2\)

\(y = 2x^2\)

Assume k = 1/2, we have:

\(y = (\frac 12x)^2\)

\(y = \frac 14x^2\)

Hence, \(y = \frac 14x^2\) is less steep than the parent quadratic equation, while \(y = 2x^2\) is steeper than the parent quadratic equation

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Answer:

Step-by-step explanation:

In a parallelogram, opposite sides are equal and parallel, which means opposite interior angles are equal.

5x - 3 = 14x - 48

-3 = 9x - 48

45 = 9x

5 = x

5(5) - 3 = 14(5) - 48

22 = 22

The value of x that would make ABCD a parallelogram is x = 5.

Hope this helps =)

95% confident that the true population mean falls within this interval.

Given:

Sample mean = 104.6

Sample standard deviation (s) = 28.8

Sample size (n) = 24

To construct a confidence interval, we need to determine the confidence level.

Step 1: t-critical value

Since the sample size is small (n < 30), we use the t-distribution.

For a 95% confidence level and a sample size of 24 (n-1 = 23) degrees of freedom

So, the t-critical value is 2.069.

Step 2: Calculate the margin of error (E)

The margin of error is given by:

E = t * (s / √(n))

E = 2.069  (28.8 / √(24)) ≈ 11.78

Step 3: Construct the confidence interval

The confidence interval is calculated as:

Lower bound = 104.6 - 11.78 = 92.82

Upper bound = 104.6 + 11.78 = 116.38

The 95% confidence interval for the population mean is (92.82, 116.38).

Thus, 95% confident that the true population mean falls within this interval.

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\( \sf \to \dfrac{n}{10} + 7 = 10\)

\( \\ \\ \)

\( \sf \to \dfrac{n}{10}= 10 - 7\)

\( \\ \\ \)

\( \sf \to \dfrac{n}{10}=3\)

\( \\ \\ \)

\( \sf \to n=3 \times 10\)

\( \\ \\ \)

\( \sf \to n=30\)

solution;

here

n/10+7=10

or n/10 =10-7

or n/10=3

n=30

Step-by-step explanation:

Answer:

YOUR ANSWER ISSS 4.

Step-by-step explanation:

B. 4

\(90+4x=4\)

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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The probability that one card drawn is 6 = 1/13.

How likely something is to happen is determined by its probability. The probability is calculated by dividing the total number of outcomes by the total number of potential events.

The likelihood is based on the range of potential outcomes. the total number of possible outcomes. As an illustration, since there is only one way to get a head and a total of two possible results, the likelihood of flipping a coin and getting heads is one in two. a tail or a head. We write P(heads) = 12 here.

Given,

the deck of 52 cards,

There are 4 sixes in total of hearts, clubs, diamonds and spades suits.

the probability that one card drawn is 6 = 4 /52 = 1/13

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24 centimeters. Hope this helped!

To derive the analytical expressions for the optimal portfolio weights of the first and second assets, we need to maximize the expected utility function.

Let's assume the weights of the first and second assets are denoted by w1 and w2, respectively. Since there is no risk-free security available, the sum of weights must be equal to 1: w1 + w2 = 1.

To find the optimal portfolio weights, we need to maximize the expected utility function with respect to w1 and w2. This can be done using optimization techniques, such as Lagrange multipliers or calculus.

We can start by taking the derivative of the expected utility function with respect to w1 and set it equal to zero to find the critical points. Similarly, we take the derivative with respect to w2 and set it equal to zero.

Next, we solve these equations to find the values of w1 and w2 that satisfy the equations. These values will give us the optimal portfolio weights for the first and second assets.

Ihe analytical expressions for the optimal portfolio weights of the first and second assets can be derived by maximizing the expected utility function and solving the resulting equations.

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Answer:

Absolute Value

Step-by-step explanation:

– The distance a number is from the zero on a number line. (Absolute value is always positive). Acute Angle - An angle with a measure > than 0° and < 90˚. Acute Triangle– A triangle that has all three angles that are acute.

The volume of the trapezoidal prism is 192 in³

A prism is a solid shape that is bound on all its sides by plane faces.

The volume of a prism is expressed as;

V = base area × height

The base of the prism is a trapezoid

area of trapezoid = 1/2(a+b)h

A = 1/2( 7+5) 4

A = 1/2 × 12 × 4

A = 12 × 2

A = 24 in²

Therefore the volume of the prism is

V = 24 × 8

V =192 in³

Therefore the volume of the trapezoidal prism is 192 in³

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Answer:

Complete question:

A coin is biased such that a head is three times as likely to occur as a tail. Find the expected number of tails when this coin is tossed twice.

Answer:

1/2

Step-by-step explanation:

Head is 3 times as likely to occur as tail;

Hence,

Sample space for 2 tosses :

{HH, HH, HH, HH, HH, HH, HH, HH, HH, HT, HT, HT, HT, HT, HT, TT}

Expected probability (E(x)) = Σx*p(x)

P(x) = required outcome / Total possible outcomes

x : __________ 0 ______ 1 _______ 2

p(x) : ________9/16_____6/16_____1/16

Σx*p(x) : 0(9/16) + 1(6/16) + 2(1/16)

= 0 + 6/16 + 2/16

= 0 + 3/8 + 1/8

= 4/8

= 1/2

Please give brainliest! :)

Answer:

-3

Step-by-step explanation:

The k value represents when the function moves up or down.

Since there are no vertical compressions or shifts, we can just focus on how much the graph went down. The function g(x) went down 3 units.

Therefore, k would equal -3.

Answer:

r = 3.25

Step-by-step explanation:

Start by eliminating the decimal fraction 0.5:  2(0.5)(r + 2.75) = 2(3) = 6

Then we have r + 2.75 = 6.

Isolate r by  subtracting 2.75 from both sides.  This leaves us with

r = 6 - 2.75 = 3.25.

r = 3.25

Answer:

27/12 KG

Step-by-step explanation:

On Sunday, Sheldon bought 4 1/2 kg of plant food. He used 1 2/3 kg on his strawberry plants and used 1/4 kg on his tomato plants. How many kilograms of plant food did Sheldon have left?

41/2 - (12/3 + 1/4)

\(1\frac{2}{3} + \frac{1}{4}\)

\(1\frac{8 + 3}{12}\) = 1 11/12

\(4\frac{1}{2} - 1\frac{11}{12}\)

\(3\frac{6-11}{12}\) = 2 7/12

The length of the kite string to the nearest metres is 57 metres

The kite is 38m above the ground. The angle the kite string makes with the ground is 42 °.

This situation forms a right angle triangle. Therefore, the length of the kite string can be found as follows;

using trigonometric ratios,

sin 42 = opposite / hypotenuse

hypotenuse side = length of the kite string

opposite side = 38 m

Therefore,

sin 42 = 38 / h

cross multiply

h = 38 / sin 42

h = 38 / 0.66913060635

h = 56.7901603575

h = 57 metres.

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Answer:

the probability is one in 6

Step-by-step explanation:

there are 6 sides on a basic die and so the only number higher than 5 is 6. you have a 1/6 chance.

Answer:

This sequence is neither arithmetic or geometric. 25 is either the 10th term, 10.2 or 10/3 either will work.