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Answer:

a) 3/2 or 1.5

b) 2/3 or ≈.66

Step-by-step explanation:

AB corresponds to DE because they are both the longest sides of their respective triangles.

a) The scale factor would be what you would multiply 8 by to get 12. 12/8 is 3/2 or 1.5

b) The scale factor would be what you multiply 12 by to get 8. 8/12 is 2/3 or ≈.66

Answer:

g(x)=x-2/x^2-9

If there is more than one value, separate them with commas.

Step-by-step explanation:

Answer:

Hey

Step-by-step explanation:

Answer:

Hi how are you

Step-by-step explanation:

I hope you have a wonderful day

Answer:

its option c kskskwoodid djekeo e ekekwl skewered dokekwowkwkw ekekekkr

Answer:

purple green blue is what it looks like

Answer:

j = $1.67

Step-by-step explanation:

total cost minus cost of chips to find cost of juice alone

$36.39 - $2.99 = $33.40

total cost of juice divided by number of bottles (20)

$33.40 ÷ 20 = $1.67

Answer: 23100 voters

Step-by-step explanation:

42*55000=2310000

2310000/100=23100 voters

Answer:

47.000 is the answer for forty seven thousands I thinj

\(\huge\color{purple}{ \colorbox{orange}{\colorbox{white} {Answer:}}}\)

\(47.000 \: would \: be \: the \: answer\)

\(\huge\color{purple}{ \colorbox{orange}{\colorbox{white} {ChaEunWoo2009}}}\)

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Scores between 23 & 59 will give Paul a C for the semester (an average between 70 and 79).

The sum of the scores on the first three, hundred point tests

= 82 + 88 + 87 = 257.

The total score required in four 100-point tests to get an average score of 70 = 70X4= 280.

The total score required in four 100-point tests to get an average score of 79 = 79X4= 316.

Therefore, the score on the fourth test should be between (280-257) & (316-57) i.e, 23 & 59 to get an average score of 70 & 79.

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Using the Factor Theorem, it is found that the complete factorization of the polynomial x³ + 8x² + 19x + 12 is given by:

A. (x+4)(x+3)(x+1)

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient.

In this problem, using a calculator, the roots of the polynomial x³ + 8x² + 19x + 12 are x = -4, x = -3 and x = -1, hence:

f(x) = (x + 4)(x + 3)(x + 1)

Which means that option A is correct.

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Answer:

Example 1: Find the perimeter of a triangle with sides measuring 5 centimeters, 9 centimeters and 11 centimeters. Solution: P = 5 cm + 9 cm + 11 cm = 25 cm

Step-by-step explanation:

Answer:

b. 25 cm

Step-by-step explanation:

P = all the sides added up

= 5 cm + 9 cm + 11 cm

= 25 cm

The simplification of the expression, ∛8x⁴y⁸ / 125 is \(\frac{2\sqrt[3]{x^{4}y^{8} } }{5}\).

The exponential expression can be solved as follows:

Therefore, let's simplify the expression.

To simplify the expression we have to deal with the exponential by applying it laws and also the cube root.

∛8x⁴y⁸ / 125

let's solve them individually,

125 = 5³ = 5 × 5 × 5

8 = 2³ = 2 × 2 × 2

Therefore,

∛8x⁴y⁸ / 125 = \(\frac{2\sqrt[3]{x^{4}y^{8} } }{5}\)

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Answer:

20√5 - 10√10

Step-by-step explanation:

6√20 + 8√5 - 5√45

first, 6√20 and 5√45 need to be simplified. 8√5 cannot be simplified any further:

6√20 = 6√4•5 = 6√2•2•5 = 6•2√5 = 12√5

5√45 = 5√8•5 = 5√2•2•2•5 = 5•2√2•5 = 10√10

now:

12√5 + 8√5 - 10√10

then, add the coefficients of 12√5 and 8√5

20√5 - 10√10

the left over numbers cannot be combined because they do not have a common radical, making 20√5 - 10√10 the final answer

Answer:

BD= 2 x 1

CA= 1 x 2

BC= 2 x 3

Step-by-step explanation:

The dimensions of the matrices BD, CA, and BC are,

2×2, 2×1, and 2×3 respectively.

Suppose we have two matrices \(A_{(m)\times(n)}\) and \(B_{(p)\times(q)}\) their multiplication is possible only when the no. of columns in the first matrix is equal to the no. of rows in the second matrix.

which is n = p and the resultant matrix will AB will have dimensions \(AB_{(m)\times(q)}\).

Given B is a 2 cross 2 matrix and D is a 2 cross 1 matrix, so the no. of columns in B is 2, and the no. of rows in matrix D is 2 so they are eligible for matrix multiplication and their resultant BD will have a dimension 2 cross 2.

Similarly, the CA matrix will have a dimension of 2 cross 1.

And, the BC matrix will have dimensions 2 cross 3.

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Answer:

Step-by-step explanation:

C

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

The unit of the rate of change is (b) dollars per month

From the question, we have the following parameters that can be used in our computation:

The table of values

Where we have

y = total amount in dollars

x = number of months

The rate of change is calculated as

Rate  = y/x

substitute the known values in the above equation, so, we have the following representation

Rate = total amount in dollars/number of months

So, we have

Unit = dollars per month

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Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Note that the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

To calculate the %DV for saturated fat, we need to first calculate how many grams of saturated fat are in the 2 tablespoon (tbsp) serving size.

From the label, we see that the serving size contains 3.5g of saturated fat.

To calculate the %DV for saturated fat, we use the equation:

%DV = (amount of nutrient per serving / DV) x 100%

Plugging in the values for saturated fat, we get:

%DV = (3.5g / 19g) x 100%

%DV = 0.1842 x 100%

%DV ≈ 18%

Therefore, the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

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Answer:

Yes. You are correct.

Step-by-step explanation:

Tan(U) = opposite / adjactent

Tan(U) = 7*√3 / 7

Tan(U) = √3

Just off the top of my head, they look right.

U = Tan-1 (√3)

U = 60

Therefore tan(W) = 90 - 60 = 30

Answer:

You end up paying 22% of the original price.

Step-by-step explanation:

The statement indicates that a store has clearance items that have been marked down by 60% and this means that you have to pay 40% of the price as:

100%-60%=40%

Now, the statement says that the are advertising an additional 45% off clearance items which means that you will have a 45% discount on the 40% of the original price. So, you have to calculate 45% of 40 and subtract that from 40 to find the percentage that you will end up paying:

40*45%=18

40-18=22

According to this, the answer is that you end up paying 22% of the original price.

Answer:

4.6

Step-by-step explanation:

Add all the numbers equaling 23 and divide it by the amount of numbers you added. 23/5=4.6

Answer:

(a) The event that represents success here is the percentage of adults who do not work at all while on summer vacation.

(b) X is a binomial random variable.

(c) The value of p for this binomial experiment is 0.30 or 30%.

(d) P(X = 3) = 0.2541.

(e) The probability that 2 or fewer of the 8 adults do not work during summer vacation is 0.5518.

Step-by-step explanation:

We are given that in a school it is found that 30% of adults do not work at all while on summer vacation. In a random sample of 8 adults, let X represent the number who do not work during summer vacation.

Let X = the number of adults who do not work during summer vacation

(a) The event that represents success here is the percentage of adults who do not work at all while on summer vacation.

(b) The conditions required for any variable to be considered as a random variable is given by;

So, in our question; all these conditions are satisfied which means X is a binomial random variable.

(c) The value of p for this binomial experiment is 0.30 or 30%.

(d) The above situation can be represented through binomial distribution;

\(P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......\)

where, n = number of trials (samples) taken = 8 adults

            r = number of success = exactly three

            p = probability of success which in our question is % of adults who

                  do not work at all while on summer vacation, i.e; p = 0.25

SO, X ~ Binom(n = 8, p = 0.30)

Now, the probability that exactly 3 adults do not work at all while on summer vacation is given by = P(X = 3)

          P(X = 3) =  \(\binom{8}{3}\times 0.30^{3} \times (1-0.30)^{8-3}\)

                        =  \(56 \times 0.30^{3} \times 0.70^{5}\)

                        =  0.2541

(e) The probability that 2 or fewer of the 8 adults do not work during summer vacation is given by = P(X \(\leq\) 2)

      P(X \(\leq\) 2) = P(X = 0) + P(X = 1) + P(X = 2)

= \(\binom{8}{0}\times 0.30^{0} \times (1-0.30)^{8-0}+\binom{8}{1}\times 0.30^{1} \times (1-0.30)^{8-1}+\binom{8}{2}\times 0.30^{2} \times (1-0.30)^{8-2}\)

= \(1 \times 0.30^{0} \times 0.70^{8}+8 \times 0.30^{1} \times 0.70^{7}+28\times 0.30^{2} \times 0.70^{6}\)

= 0.5518

Answer:

Step 2

1 2/3 was converted as 5/2 instead of 5/3

Step-by-step explanation:

Number of batches

Solution by Janice:

Error made at step 2:

1 2/3 was converted as 5/2 instead of 5/3

Answer:

A

Step-by-step explanation:

Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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