12. FIND THE ERROR A student is finding the
total cost c, including sales tax, of a book
that costs $9.95. The sales tax rate is 9%.
Find the student's mistake and correct it.

Answer:

Answer:

  $45

Step-by-step explanation:

($9 /h)(5 h) = $45

Jaylen earns $45 for working 5 hours.

Answer:

45$

Step-by-step explanation:

If she works 5 hours and gets 9$ per hour, you multiply 9 x 5 = 45.

Answer:

The correct option is;

pH = 4.1

Step-by-step explanation:

The given information are;

The hydrogen ion [H⁺] concentration in tomato juice = \(10 ^{-4.1}\)

The pH of a solution = -㏒{H⁺] =  -㏒( \(10 ^{-4.1}\)) = -(-4.1) × ㏒(10) = 4.1

The pH of the of the tomato juice = 4.1

The pH is the term used to refer to the acidity of water with the range of pH values ranging from 0 to 14 where pH values of a solution lesser than 7 are considered acidic while pH values above 7 indicate a basic solution.

Answer:

y = 5x - 3, so M = 5 and C = -3.

Answer:

x = 9

Step-by-step explanation:

Ratios!! Since both triangles are in the same triangle, they are proportinate in size. from there, we can match the sides of the small triange to the sides of the large.

\( \frac{4}{10} = \frac{6}{6 + x} \)

Then, you can cross multiply and solve the equation algebraicly for x.

4(6+x) = 60

24+4x = 60

4x = 36

x = 9

The negative correlation between IQ and age guarantees that all younger people have higher IQ's than older people.

The strength of the linear link between two separate variables, x and y, is shown by correlation coefficients. A positive association is shown by a linear correlation coefficient larger than zero. Indicating a negative association is a value less than zero. The two variables x and y do not have any relationship when their values are 0, to sum up.

A positive correlation indicates that both variables move in the same direction when the correlation value is higher than 0. When is 1, it denotes a complete positive association between the two variables under comparison; when one variable rises or falls, the other one rises or falls in the same direction and by the same amount.

When the correlation coefficient is less than 0, there is a negative (inverse) correlation. This suggests that both variables are moving in the obverse direction. In essence, any reading between 0 and -1 denotes an opposing movement of the two securities. The connection is said to as fully negatively correlated when is equal to -1.

Thus, the negative correlation between IQ and age guarantees that all younger people have higher IQ's than older people.

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3(2)-2=4, the second is true. the answerb is b

the Numbers of days = 3

The second statement(She raised $0.50 for each 1/3 of mile that she walked) means

1/3 miles = $0.50

For first day walk we have:

1/3 miles = $0.50

12 miles = 12 x 0.50 x 3 = $18

For Second day walk we have:

1/3 miles = $0.50

8miles = 8 x 0.50 x 3 = $12

For Third day walk we have:

1/3 miles = $0.50

16miles = 16 x 0.50 x 3 = $24

The amount she raised for the three days becomes

$18 + $12 + $24

=$54

\( \tan(60) = \frac{x}{ \sqrt{7} } \)

\( \sqrt{3} = \frac{x}{ \sqrt{7} } \)

\(x = \sqrt{21} \)

\(\frak{\fcolorbox{black}{pink}{Black Pink in your area$~$}}\) ~←(>▽<)ﾉ

Answer:

√21

Step-by-step explanation:

30, 60, 90 triangle

Across from 30 is a, across from 60 is a√3

So, √7√3 is √21

The capacity of the smaller container is 352 ml. Their volumes are related by the cube of their corresponding linear dimensions.

Since the two containers are mathematically similar, their volumes are related by the cube of their corresponding linear dimensions. Let V1 be the volume of the smaller container and V2 be the volume of the larger container. Let h1 and h2 be the heights of the smaller and larger containers, respectively. Then we have:

V1/V2 = (h1/h2)^3

We know that h1 = 30cm and h2 = 75cm, and V2 = 5.5 litres = 5500 ml. Substituting these values, we get:

V1/5500 = (30/75)^3

V1/5500 = 0.064

Multiplying both sides by 5500, we get:

V1 = 352 ml

Therefore, the capacity of the smaller container is 352 ml.

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Answer:

4a + 4b - 2

Step-by-step explanation:

To evaluate h(a + b) , substitute x = a + b into h(x), that is

h(a + b) = 4(a + b) - 2 = 4a + 4b - 2

Step-by-step explanation:

We need to use the binomial theorem/Pascal's triangle here.

(a+b)^5 = (5 choose 0)a^5 + (5 choose 1)a^4*b + (5 choose 2)a^3*b^2 + (5 choose 3)a^2*b^3 + (5 choose 4)a*b^4 + (5 choose 5)b^5.

5 choose 0 = 1

5 choose 1 = 5

5 choose 2 = 10

5 choose 3 = 10

5 choose 4 = 5

5 choose 5 = 1

And 1, 5, 10, 10, 5, 1, is the (5+1) = 6th row of pascal's triangle.

Therefore we get

g^5 + 5g^4*2 + 10g^3*2^2 + 10g^2*2^3 + 5g*2^4 + 2^5

which is

g^4 + 10g^4 + 40g^3 + 80g^2 + 80g + 32

Or, you could do the slow way, by just doing (g+2)(g+2)(g+2)(g+2)(g+2)

Formula to convert milligrams to micrograms: Number of micrograms = Number of milligrams x 1000

To convert milligrams (mg) to micrograms (μg), you need to multiply the number of milligrams by 1000. This is because there are 1000 micrograms in one milligram.

Here is the formula:

Number of micrograms = Number of milligrams x 1000

For example, let's say you want to convert 5 milligrams to micrograms. You would use the formula as follows:

Number of micrograms = 5 mg x 1000 = 5000 μg

Therefore, 5 milligrams is equal to 5000 micrograms.

It's important to pay attention to the units when making conversions, as mixing up units can lead to errors in calculations.

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Answer:

the x

Step-by-step explanation:

Looking at the x in an equation can reveal its shape. A linear graph can look like y=x, y=mx, y=mx+b (m being any number).

When you look at graphs that aren't linear, the x doesn't stand alone in the equation.

Parabolas have a y=x^2 equation. Cubic graphs are y=x^3. They have something attached to the x.

To see all the different kinds of equations and what their graphs look like you can search up "parent functions" and all the basic formulas show up.

Answer:

1,290.32

Step-by-step explanation:

508 x 2.54

Answer:

200

Step-by-step explanation:

divide 508 by 2.54 and boom answer.

If you are confused on long division you can message me and I can try to help.

The unknown number is -9.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, the product of a number and -7 is 63.

Let the unknown number be x.

Now, -7×x=63

-7x=63

x= -9

Therefore, the unknown number is -9.

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John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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Answer:

c (the third option)

Step-by-step explanation:

Answer:

-2/3x+1

Step-by-step explanation:

Answer: 3rd brand.

Step-by-step explanation:

1st brand:

6 oz cost $1.25

The amount per ounce will be:

= $1.25/6

= $0.21

2nd brand:

8 oz cost $1.33

The amount per ounce will be:

= $1.33/8

= $0.17

3rd brand:

12 oz cost $1.50

The amount per ounce will be:

= $1.50/12

= $0.125

4th brand:

16 oz cost $2.10

The amount per ounce will be:

= $2.10/16

= $0.13

From the calculation, the 3rd brand of orange juice is the better but as it's cheaper than others.

The sequence of transformations used to show the congruence of polygons JKLMN and PQRST is to reflect PQRST across the y-axis and then translate the result down 10 units.

We are given two polygons. Both the polygons are congruent, and to prove it, we can use the concept of transformations. The first transformation we need to perform is to reflect the polygon PQRST across the y-axis. The next transformation that needs to be performed is to translate the result down by 10 units. We find that the polygon PQRST now coincides with the polygon JKLMN. Hence, it is proved that the polygons are congruent to each other.

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As the alternate hypothesis is a two-tailed test the p-value for this hypothesis test is 0.0512.

Here the null hypothesis, H₀, is μ₁ =μ₂

    Alternate hypothesis,  H₁ , is  μ₁ ≠ μ₂

The statistical test is said to be a two-tailed test. So the critical area of of distributions are on both sides of the range.

Here t test-ind method for spicy module is used.

The output is given as (-1.99 , 0.0512)

In such an output the first value is the test statistic value and second value is the p-value.

So the test statistic value = -1.99

p-value = 0.0512.

So the p-value is 0.0512.

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Answer:

x = 3.5

Step-by-step explanation:

Given

\(3^{2x-5}\) = 9 , that is

\(3^{2x-5}\) = 3²

Since the bases on both sides are equal, both 3 , then equate the exponents

2x - 5 = 2 ( add 5 to both sides )

2x = 7 ( divide both sides by 2 )

x = 3.5

It will take approximately 3.96 years (or approximately 3 years and 11 months) for Vincent's savings to reach $9,000.

To solve this problem, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

Where:

FV = Future Value

P = Payment (deposit amount)

r = Interest rate per compounding period

n = Number of compounding periods

In this case, Vincent deposits $165 at the end of each quarter, so P = $165. The annual interest rate is 6%, compounded quarterly, so the interest rate per compounding period, r, would be 6% divided by 4 (since there are 4 quarters in a year), which is 0.06/4 = 0.015.

We want to find the number of years, n, it will take for Vincent's savings to reach $9,000. Let's substitute the given values into the formula and solve for n:

9,000 = 165 * [(1 + 0.015)^n - 1] / 0.015

To solve this equation, we can use algebraic techniques or a financial calculator. Solving the equation, we find that n is approximately 15.83.

Since n represents the number of quarters, we need to convert it to years by dividing it by 4 (since there are 4 quarters in a year):

n (in years) = 15.83 / 4 ≈ 3.96

Therefore, it will take approximately 3.96 years (or approximately 3 years and 11 months) for Vincent's savings to reach $9,000.

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Answer:

Step-by-step explanation:

Your answer

Regular price = x

Discount price =0.2x

Price = x- 0.2x = 0.8x $

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False. Just because two vectors are eigenvectors of the same matrix with different eigenvalues, it does not mean they are orthogonal to each other.

Eigenvectors of a matrix are vectors that, when the matrix is multiplied by them, the vector remains the same except for a scaling factor. Eigenvalues are the scaling factors of the eigenvectors. If two eigenvectors, v1 and v2, of a 4x4 matrix a have eigenvalues 1 and 2 respectively, it does not mean that they are orthogonal (i.e. at a 90 degree angle) to each other. Orthogonality is a property of two vectors that is independent of the matrix and can only be determined by calculating the dot product of the two vectors. Therefore, two eigenvectors of the same matrix with different eigenvalues may or may not be orthogonal to each other.

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Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer: 16

Step-by-step explanation:

multiplying by negative exponents can be a little tricky. So (1/4x)^-2 becomes 16/x^2 = __/x^2 so the missing number is 16

In reality, however, the two drugs do not differ. This is an example of a Type I errors.

In statistics, a Type I error, also known as a false positive or alpha error, occurs when a null hypothesis that is actually true is rejected. In the context of the given randomized trial, the null hypothesis states that there is no difference between the efficacy of the two drugs.

However, due to random chance or other factors, the trial yielded a statistically significant difference (with a P value < 0.05) between the drugs, leading to the rejection of the null hypothesis.

In reality, since the two drugs do not actually differ in efficacy, the observed difference is likely due to random sampling variability or experimental error. A Type I error can occur when the significance level (alpha) used in the hypothesis test is set too low, leading to a higher likelihood of rejecting the null hypothesis incorrectly.

It is essential to consider Type I errors and carefully interpret the significance of study findings to avoid drawing erroneous conclusions based on statistical significance alone.

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