What is the sales tax for a dress that costs 37.99 and a pair of shoes that cost 39.99. The sales tax is 8.25%.

Answer:

et's solve your equation step-by-step.

(x+3)2−1=35

Step 1: Simplify both sides of the equation.

x2+6x+8=35

Step 2: Subtract 35 from both sides.

x2+6x+8−35=35−35

x2+6x−27=0

Step 3: Factor left side of equation.

(x−3)(x+9)=0

Step 4: Set factors equal to 0.

x−3=0 or x+9=0

x=3 or x=−9

Answer:

x=3 or x=−9

Answer:

Add 1 to each side

Take the square root of each side

Subtract 3 from each side

Step-by-step explanation:

(x+3)^2  -1 = 35

Add 1 to each side

(x+3)^2  -1+1 = 35+1

(x+3)^2   = 36

Take the square root of each side

sqrt ((x+3)^2)   =±sqrt (36)

x+3 = ±6

Subtract 3 from each side

x+3-3 = -3±6

x = -3±6

x = -3+6          x = -3-6

x = 3                x = -9

There are 12 cellists

Answer:

5/4

Step-by-step explanation:

A ratio can be written with a colon or as a fraction. Fractions can also be simplified further into the desired ratio.

Please let me know if this helped!!!

It is false that mobile banner ads perform significantly better than desktop banners.

There is no clear consensus on whether mobile banner ads or desktop banner ads perform better. The effectiveness of banner ads depends on various factors such as the placement of the ad, its design, and the target audience.

However, it is true that mobile usage has been increasing rapidly in recent years, and more people are accessing the internet through their mobile devices than through desktop computers. Therefore, it is important for advertisers to optimize their ads for mobile devices and ensure that they are mobile-responsive.

Nevertheless, it cannot be generalized that mobile banner ads are more effective than desktop banner ads. The effectiveness of an ad should be evaluated on a case-by-case basis, taking into account the specific objectives, target audience, and design of the ad.

Therefore, it is important for advertisers to test their banner ads on both desktop and mobile devices to determine which platform works best for their specific campaign. And the given statement is false.

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The exponential equation that models Isabella's weekly sales, S(w) in dollars, w weeks after opening her shop can be written as:

S(w) = ab^w; where a is the initial sales in the first week, and b is the rate of increase per week as a decimal.

We know that her sales in the first week were $86, so a = 86. And we also know that her sales increased by 20% the following week, so her sales in the second week were 1.2 times her sales in the first week, or 1.2 x 86 = $103.2.

To find b, we can use the fact that her sales continued to increase at the same rate each week. That means that the ratio of her sales in any two consecutive weeks is the same. So we have:

S(w+1)/S(w) = 1 + b

103.2/86 = 1 + b

b = 0.2

So the exponential equation that models Isabella's weekly sales is:

S(w) = 86 x 1.2^w

Therefore, the equation S(w) = 86 x 1.2^w will give the sales in dollars for any number of weeks w after Isabella opened her shop.

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Answer:

227.5

Step-by-step explanation:

Find the number that is increased by 30% to get to 325.  

100-30 = 70.

In other words, what number is 70% of 325.

325 x .70 = 227.5

The original price of the ring was 227.5.

Check your work, 227.5 = 70% of X

227.5  / .70  = 325

Answer:

The cost before the increase is £250.

Step-by-step explanation:

Given that after 30% increases, the cost of the ring is £325 so we can assume that 130% is £325. Now, we have to form an expression in term of x where x represents the original cost :

\( \frac{130}{100} \times x = 325\)

Next, we have to solve it :

\(x = 325 \div \frac{130}{100} \)

\(x = 325 \times \frac{100}{130} \)

\(x = 250\)

the answer would be 1/4.

∠C ≅ ∠F is congruent to show that ΔABC ≅ ΔDEF

ΔABC ≅ ΔDEF

Therefore,

AAS congruence rule or theorem states that if two angles of a triangle with a non-included side are equal to the corresponding angles and non-included side of the other triangle, they are considered to be congruent.

Therefore,

∠C ≅ ∠F

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Answer:

she sold 21 teeshirts

Step-by-step explanation:

y=5x -22 is the equation for the cost of the  tee shirts for her (22) and the cost for others(5x bc we dont know the amount shes sold yet).

if she made 85 dollers in profit shehad already paid off the 22 dollars it cost.

So you would add 22+83. which would equal 105.  then divide 105 by 5 for the number of tee shirts she sold. 105/5 =21

Answer:

B or D if mulptie choice

Step-by-step explanation:

Principal Component Analysis (PCA) is a dimensionality reduction technique used to simplify complex datasets while retaining important information. It achieves this by transforming the original variables into a new set of variables called principal components.

These principal components are linear combinations of the original variables and are designed to capture the maximum amount of variance in the data.

Here's a detailed explanation of the steps involved in PCA:

1. Standardize the data:

  First, the dataset is standardized by subtracting the mean from each variable and dividing by the standard deviation. Standardizing the data ensures that each variable contributes equally to the analysis and prevents variables with larger scales from dominating the results.

2. Compute the covariance matrix:

  The covariance matrix is calculated based on the standardized data. It represents the relationships between different variables in the dataset. The covariance between two variables measures how they vary together. A positive covariance indicates that the variables tend to increase or decrease together, while a negative covariance indicates an inverse relationship.

3. Compute the eigenvectors and eigenvalues:

  The eigenvectors and eigenvalues are calculated from the covariance matrix. Eigenvectors represent the directions in the dataset along which the data varies the most. Each eigenvector corresponds to an eigenvalue, which represents the amount of variance explained by the respective eigenvector. The eigenvectors are sorted in descending order based on their corresponding eigenvalues.

4. Select the principal components:

  The principal components are selected based on the eigenvalues. The first principal component (PC1) corresponds to the eigenvector with the largest eigenvalue and captures the most variance in the data. Subsequent principal components capture decreasing amounts of variance. Typically, a subset of principal components that explain a significant portion (e.g., 95%) of the total variance is chosen.

5. Transform the data:

  The original data is transformed into the new coordinate system defined by the principal components. This transformation involves multiplying the standardized data by the matrix of selected eigenvectors. The resulting transformed data contains the scores along the principal components.

PCA is useful for various purposes, including dimensionality reduction, data visualization, and feature extraction. It allows for the identification of patterns and relationships within the dataset while reducing the dimensionality of the data, which can be beneficial in computational efficiency and interpretation.

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246 (approx) is the minimum sample size when we want to construct.

What does a statistical sample distribution mean?

The process of regularly sampling a certain population yields a sampling distribution, which is an accurate probability distribution of a statistic. It displays a range of possible outcomes for a statistic, such as the mean or mode of a variable for a population. With each selected random sample, a different value may be assigned to the statistic under inquiry.

MOE = z*s.d/√(n)

95% CI, z = 1.96

s.d = √(0.64*0.36) = 0.48

0.06 = 1.96*0.48/√(n)

So n = 245.86 = 246 (approx)

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Answer: 11 hours :)

Step-by-step explanation: 1215-445=770, 770 divided by 70=11 so 11 days

The cost of "x" radios is $10x and transportaiton fee of $5. So cost equation for "x" radios is,

(b)

The selling price of one radio is $12. So for "x" radio Profit(selling price) equation is,

(c)

Determine the value of x for which profit equation is equal to cost equation.

The number of radios can never be in fraction. So individual has to buy 3 radios to have equal cost and profit,.

Answer:

I think the answer is ...

100×100=10,000

The solution is: the equation of the circle with radius 8 and center (1, 3) is: x² + y² - 2x - 6y - 54 = 0.

Here, we have,

Given ,

the circle with radius 8 and center (1, 3).

so, we have,

the center of circle (h,k) = (1,3) and radius, r = 8

we know that,

Equation of the circle = (x-h)² + (y-k)² = r²

so, we get,

⇒ (x - 1)² + (y - 3)² = 64

⇒ x² - 2x + 1 + y² - 6y + 9 = 64

⇒ x² + y² - 2x - 6y - 54 = 0 (on simplification)

Hence, The solution is: the equation of the circle with radius 8 and center (1, 3) is: x² + y² - 2x - 6y - 54 = 0.

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Answer:

$4.5

Step-by-step explanation:

18 muffins divided by 6 people = 3 muffins per person

If you divide 27 and 6,  it equals $4.5

Each person would have to pay $4.5.  

Hope this helps! Have a great day :)

xy + xz is an even integer & x is even and y + xz is an odd integer &  either (x-1) is even or (y-z) is even .

1. xy + xz is an even integer - SUFFICIENT

Given:

xy + z is odd ...(i)

xy + xz is even ...(ii)

subtracting (ii) from (i)

we get xz - z, which should be odd (* since odd - even = odd)

=> z(x-1) is odd

=> both z and (x-1) is odd

=> since (x-1) is odd, x must be even.

2. y + xz is an odd integer -INSUFFICIENT

Given:

xy + z is odd ...(i)

y + xz is odd ...(ii)

subtracting (ii) from (i)

we get xy + z - y - xz

= (x-1)(y-z) , which should be even

=> either (x-1) is even or (y-z) is even ....insufficient to determine

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There are 8 teams left after 4 rounds.

Given that there are 128 teams entered in a basketball tournament, and half of the teams are eliminated each round, to determine how many teams are left after 4 rounds, the following calculation must be performed:

Therefore, there are 8 teams left after 4 rounds.

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a) The population is the set of all widgets sold by the company.

(b) The variable is the percentage of widgets sold at the Boston location.

(c) The variable is quantitative.

(d) The parameter is the true percentage of widgets sold at the Boston location.

a The population is the set of all widgets sold by the company. This is because we are interested in the percentage of all widgets sold at the Boston location, and the only way to know this is to look at the entire population of widgets sold.

b. The variable is the percentage of widgets sold at the Boston location. This is because we are interested in the proportion of widgets sold at the Boston location out of the total number of widgets sold.

c The variable is quantitative because it can be measured numerically. We can say that 34% of widgets were sold at the Boston location, or that 27% of widgets were sold at the Boston location in the sample.

d The parameter is the true percentage of widgets sold at the Boston location. This is because the parameter is the actual value of the variable in the population, as opposed to the value of the variable in the sample.

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Answer: 1,2,3,5,6, 10, 15, 30

Step-by-step explanation: Simply find which number is divisible by 30

Answer:

1, 2, 3, 5, 6, 10, 15 and 30.

Step-by-step explanation:

The factors of 30 are the numbers that divide 30 exactly (without leaving a remainder).

Answer: 5.78 × 10 to the negative ninth power

Step-by-step explanation:

Solution:

Given the absolute value parent function below

If the function is vertically compressed by a factor of 4, the function becomes

Where

Hence, the answer is

Option A

We're given:

\((3f-4g)(t)\) is the same as \(3f(t)-4g(t)\). Now, we can just plug in the functions as if they're variables in an equation.

\(3f(t)-4g(t)\)

\(= 3(4t-2)-4(2t+2)\\= 12t-6-8t-8\\= 4t-14\)

\((3f-4g)(t)= 4t-14\)

Yes, the instructor should use linear regression to predict exam scores for a student who studied 10 hours for the final.

A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

Nonlinear regression uses a curve to associate the variables, whereas linear regression uses a straight line.

If a clear linear relationship can be shown on the scatterplot, linear regression may be useful. The use of linear regression is appropriate because there is a high correlation. So, it is concluded that it is beneficial for instructor to use linear regression.

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The number of 40-kilogram crates that can be loaded into the shipping containe is 272.5.

Two or more expressions with an equal sign is called as Equation.

Given data :

Weight of the crate = 40 kg

Greatest weight that the container can load = 23000 kg

Weight of the other shipments on the container = 12100 kg

So the greatest number of 40 kg crates = c

Therefore, the weight of the other shipment + weight of crate x number of crates ≤ greatest weight of the container

12100 + (40 x c) ≤ 23000

12100 + 40c ≤ 23000

40c ≤ 23000 - 12100

40c ≤ 10900

c ≤ 272.5

Hence, the maximum number of 40 kg crate is 272.5.

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When rotated about its center, a regular hexagon has 6 rotational symmetries. in addition to rotational symmetry, a regular hexagon has 6 lines of reflectional symmetry.

a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

When a regular hexagon is rotated about its center, it has 6 rotational symmetries, one for each angle of 60 degrees.

In addition to rotational symmetry, a regular hexagon also has 6 lines of reflectional symmetry. Each line of symmetry passes through the center of the hexagon and two opposite vertices, dividing the hexagon into two congruent halves.

Hence, when rotated about its center, a regular hexagon has 6 rotational symmetries. in addition to rotational symmetry, a regular hexagon has 6 lines of reflectional symmetry.

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The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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The correct answer is (c) depending on the benchmark interest rates. The liquidity premium can be positive or negative, depending on market conditions and the risk associated with specific securities.

It seems like there are some typos in your question, but I believe you're asking about the liquidity premium when the yield curve is inverted. In this context, I'll include the terms "ratio," "liquidity, and "negative" in my answer.

The liquidity premium is the additional return that investors demand by holding securities with lower liquidity or higher risk. When the yield curve is inverted, it generally indicates that short-term interest rates are higher than long-term interest rates. This can be a result of higher demand for long-term bonds, which drives their prices up and yields down.

In such a situation, the liquidity premium is:

a) not always negative, because an inverted yield curve doesn't necessarily mean that the liquidity of the market is negatively impacted. The ratio of liquid to illiquid assets can still be favorable even when the yield curve inverts.

b) not always positive, as the premium depends on the overall market conditions and risk factors associated with specific securities.

c) It depends on the benchmark interest rates, which are a key determinant of the yield curve shape. When benchmark interest rates change, the yield curve can either steepen, flatten, or invert, affecting the liquidity premium accordingly.

So the correct answer is (c) depending on the benchmark interest rates. The liquidity premium can be positive or negative, depending on market conditions and the risk associated with specific securities.

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