The variable t in the formula d = rt stands for

Answer:

About 405

Step-by-step explanation:

570 CDs were sold the first quarter.

The second quarter CDs had dropped 29% from the first quarter (570).

Dropped, you should think you are subtracting.

So we need to

simplify 570-.29(570):

570(1-.29)

570(.71)

404.7

404.7 --> 405 (when rounded)

In order to find the answer to your question, we would need to find how much of 570 is 29%, and subtract that number to 570.

The reason why we would do this is because in the question, it says that the sales dropped 29% for one quarter to the next. This means that the next quarter would drop 29%.

We know that they sold 570 units, so we would use 570 in our calculations.

We know that the sales decrease by 29%, so we would multiply 570 by 0.29 to find how much of 570 is 29%.

[tex]570*0.29=165.3[/tex]

29% of 570 is 165.3

What we would do now is subtract 570 by 165.3 in order to fin how much sales they made in the next quarter.

[tex]570-165.3=404.7[/tex]

Once you're done solving, you would get the answer of 404.7

This means that they sold 404.7 (405 when rounded) CDs in the next quarter.

Answer:

[tex]f(x) = 7x + 30[/tex]

Step-by-step explanation:

We need at least two points to write the equation of a straight line.

The recursive formula that Elijah wrote is:

[tex]f(0) = 30[/tex]

[tex]f(n + 1) = f(n) + 7[/tex]

When we substitute n=0, we get:

[tex]f(0 + 1) = f(0) + 7[/tex]

[tex]f(1) = 30 + 7[/tex]

[tex]f(1) = 37[/tex]

The points (0,30) and (1,37) lies on this line.

The equation of this line is of the form:

[tex]f(x) = mx + b[/tex]

where b =30 is the y-intercept and m=7 is the slope.

We plug in these values to get:

[tex]f(x) = 7x + 30[/tex]

Note that the slope of the line is equal to the common difference of the Arithmetic Sequence.

You could also use the two points to find the slope:

[tex]m = \frac{37 - 30}{1 - 0} = 7[/tex]

Rewrite the equation in slope-intercept form:

y+5=2(x+1)

Use the distributive property:

y+5 = 2x +2

Subtract 5 from each side:

y = 2x -3

The slope is the value with the X

The slope = 2

Answer:

2.5

Step-by-step explanation:

2(x+1)=y+5

2x+1=y+5

y+5=6

in addtion y can be add

so we have now...

2x+1=6

minus 1 from 6 and get 5

2x=5

5 divide by 2 = 2/5

Hope it helps

Answer: Not sure if I’m correct but I’m pretty sure

x = 90

Step-by-step explanation:

Total figure = 360 degrees

107+72+91=270

360-270=90

Answer:

x=90 degrees

Step-by-step explanation:

The sum of the 4 angles of a quadrilateral add to 360 degrees

Add the 4 angles

72+107+x+91 = 360

Combining like terms

270 +x = 360

Subtract 270 from each side

270+x-270 = 360-270

x = 90

The unknown angle is 90

Answer:

A.

5 ^ (5/6)

Step-by-step explanation:

5 ^ (1/2)  * 5 ^ (1/3)

We know that a^b * a^ c = a ^ (b+c)

5 ^ (1/2 + 1/3)

5^ (3/6+2/6)

5^ (5/6)

Answer:

5^(5/6)

Step-by-step explanation:

5^(1/2)*5^(1/3)=5^(1/2+1/3)=5^(5/6)

When multiplying numbers with same base you add the exponents.

Answer:

m = 200

Step-by-step explanation:

30 m = 6000 Divide both sides by 30

30 m / 30 = 6000 / 30

m = 200

Answer:

[tex]1000(.95)^h[/tex]

Step-by-step explanation:

[tex]h(t)=A \cdot B^t[/tex] is an exponential equation where A is the beginning amount and B is the rate that the population grows or dies.

So we start with 1000 bacteria, they are giving us A.

The bacteria population is decreasing because they are dying 5% each hour.

So that is after the first hour we have 1000-.05(1000) or 1000(1)-1000(.05)=1000(1-.05)=1000(.95).

We will keep multiplying by .95 per hour. 0.95 is the repeated factor.

That is the function is [tex]1000(.95)^h[/tex].

If you let h=0 which means 0 hours has happened, you will see the bacteria is 1000 as desired. 1000(.95)^0=1000(1)=1000.

The bacteria population can be determined using the formula (ℎ)=1,000·0.95^ℎ, which represents exponential decay at a rate of 5% each hour. therefore, option D is correct

To determine the bacteria population after a number of hours, we need to use the formula (ℎ)=1,000·0.95^ℎ. This formula represents the exponential decay of the bacteria population at a rate of 5% per hour. The initial population is 1,000, and each hour the population decreases by 5% (or 0.95).

For example, after 1 hour, the population can be calculated as (1,000)·(0.95)^1 = 950 bacteria. After 2 hours, the population would be (1,000)·(0.95)^2 = 902.5 bacteria, and so on.

Therefore, the correct answer is (d) (ℎ)=1,000·0.95^ℎ.

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Given that area of circle is 64cm we can assume we will need to first find radius and then calculate circumference.

First we know that area of a circle is [tex]A=\pi r^2[/tex] hence [tex]r=\sqrt{\dfrac{A}{\pi}}[/tex]

We can now put in our area,

[tex]r=\sqrt{\dfrac{64}{\pi}}\approx20.37[/tex]

Then we use the formula for circumference,

[tex]C=2\pi r\Longrightarrow C=2\pi\cdot20.37\approx\boxed{128\mathbf{cm}}[/tex]

Hope this helps.

r3t40

Answer:

Step-by-step explanation:

Add all 8/20 marbles multiply Times 5 40/100 = 40%

Answer =40%

Answer:

2x^3 - 6x^2 - 4x + 12.

Step-by-step explanation:

(p*q) (x)  = (2x^2 - 4)(x - 3)

= 2x^3 - 6x^2 - 4x + 12.

For this case we have the following functions:

[tex]p (x) = 2x ^ 2-4\\q (x) = x-3[/tex]

We must find [tex](p * q) (x).[/tex] For definition, we have to:

[tex](p * q) (x) = p (x) * q (x)[/tex]

So:

[tex](p * q) (x) = (2x ^ 2-4) (x-3)[/tex]

We apply distributive property:

[tex](p * q) (x) = 2x ^ 3-6x ^ 2-4x + 12[/tex]

Answer:

[tex](p * q) (x) = 2x ^ 3-6x ^ 2-4x + 12[/tex]

Answer: vertical angles are congruent.

Step-by-step explanation:

Answer: Vertical angles are congruent.

Step-by-step explanation:

Given : Line A and line Bare parallel.

To prove : ∠1≅∠2

We know that when two lines crosses each other, they make vertically opposite angles.

In picture , we have ∠2 and ∠3 are vertical angles.

And it is known that the vertical angles are congruent.

Therefore, ∠2 ≅ ∠3

So the correct reason to the statement "∠2 ≅ ∠3" is "Vertical angles are congruent."

Answer:

25.9

Step-by-step explanation:

12+7x−(1−3) (evaluate parentheses first)

= 12+ 7x - (-2)

= 12+ 7x + 2

= 14+ 7x

When x = 1.7, equation becomes

14+ 7(1.7)

= 14 + 11.9

= 25.9

Answer:

D) 160π/3 units²

Step-by-step explanation:

Step 1: Write the formula for area of sector

Area of sector = 1/2 x r² x angle in radians

Step 2: Substitute values in the formula

Area of sector = 1/2 x 8² x 5π/3

Step 3: Solve to find the value of area of sector

Area of sector = 160π/3 units²

Therefore, the correct option is D

!!

[tex]\bf \underset{\textit{\Large 18 + 8 = 26 units}}{\stackrel{\textit{18 units}}{\boxed{-18}\rule[0.35em]{10em}{0.25pt}}0\stackrel{\textit{8 units}}{\rule[0.35em]{5em}{0.25pt}\boxed{8}}}[/tex]

Answer:

Step-by-step explanation:

The ruler Postulate:

the distance between number A and number B

AB = |B - A|

We have A = -18 and B = 8. Substitute:

|8 - (-18)| = |8 + 18| = |26| = 26

Answer:

[tex]-6y^2+5y+2[/tex]

Step-by-step explanation:

I'm assuming you want to simplify:

[tex]3y^2+5y-(4y^2+5)-8y^2-(-7-3y^2)[/tex]

Distribute to get rid of the ( ):

[tex]3y^2+5y-4y^2-5-8y^2+7+3y^2[/tex]

Put like terms together:

[tex]3y^2-4y^2-8y^2+3y^2+5y-5+7[/tex]

Combine the like terms:

[tex]-6y^2+5y+2[/tex]

A (x=y)

By vertical angles, the angle opposite y is equal to y, and x = y because it would transform isometrically onto x (as can be seen by the parallel lines because the transversal can be treated as parallel to itself)

Answer:

(6,∞)

x > 6

Step-by-step explanation:

Solve by adding 4 to both sides.

[tex]x-4>2\\x>6[/tex]

To put this in interval notation for your solution set, consider your sign.

You have a greater than sign, which means that 6 is not a solution. In interval notation, that means that you should use parentheses " ( " instead of brackets " [ ".

Your solution set goes on infinitely, and infinity also uses parentheses rather than brackets.

You can write your solution set in interval notation as follows:

(6, ∞)

Answer:

it is not possible that Brayden made it back to his starting point.

Step-by-step explanation:

Part 1: Step 1: Define the map scale

REAL:MAP

1 km : 1 cm

5 km : 5 cm

14 km : 14 cm

8 km : 8 cm

Step 2: Sketch the map according to the scale.

Shown on the map in the picture attached.

Part 2: As shown on the map, it is not possible that Brayden made it back to his starting point.

!!

Answer:

B. -2√2 - 5

C. 2√2 - 5

Step-by-step explanation:

The left side of the equation is already a perfect square.

Let us factorize it first.

x²+10x+25=8

x(x+5)+x(x+5)=8

(x+5)²=8

Let us take the square roots of both sides.

x+5=±√8

But √8=±2√2

Therefore in surd form, the two solutions become:

x+5=2√2 or x+5=-2√2

Therefore x= 2√2-5 and -2√2+-5

Answer:

[tex]\large\boxed{-mn+10m+5n}[/tex]

Step-by-step explanation:

[tex](14mn - 12m +7n)-(15mn - 22m +2n)\\\\=14mn-12m+7n-15mn-(-22m)-2n\\\\=14mn-12m+7n-15mn+22m-2n\qquad\text{combine like terms}\\\\=(14mn-15mn)+(-12m+22m)+(7n-2n)\\\\=-mn+10m+5n[/tex]

[tex]\bf \left( y^{\frac{4}{3}}xy^{\frac{2}{3}} \right)^{-\frac{1}{2}}\implies \left( y^{\frac{4}{3}}y^{\frac{2}{3}}x \right)^{-\frac{1}{2}}\implies \left( y^{\frac{4}{3}+\frac{2}{3}}x \right)^{-\frac{1}{2}}\implies \left( y^{\frac{6}{3}}x \right)^{-\frac{1}{2}} \\\\\\ (y^2x^1)^{-\frac{1}{2}}\implies \left( y^{-\frac{1}{2}\cdot 2}x^{-\frac{1}{2}\cdot 1} \right)\implies y^{-1}x^{-\frac{1}{2}}\implies \cfrac{1}{y}\cdot \cfrac{1}{x^{\frac{1}{2}}}\implies \cfrac{1}{y\sqrt{x}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\\\\a^n\cdot a^m=a^{n+m}\\\\(a^n)^m=a^{nm}\\\\a^{-1}=\dfrac{1}{a}\\============================\\\\\bigg(y^\frac{4}{3}\cdot y^\frac{2}{3}\bigg)^{-\frac{1}{2}}=\bigg(y^{\frac{4}{3}+\frac{2}{3}}\bigg)^{-\frac{1}{2}}=\bigg(y^{\frac{4+2}{3}}\bigg)^{-\frac{1}{2}}\\\\=\bigg(y^{\frac{6}{3}}\bigg)^{-\frac{1}{2}}=\bigg(y^2\bigg)^{-\frac{1}{2}}=y^{(2)\left(-\frac{1}{2}\right)}=y^{-1}=\dfrac{1}{y}[/tex]

Answer:

They must mix

_44_ pounds of the Organic Free Trade Blend

_36__ pounds of the Rift Valley Blend.

Round your answers to the nearest whole number of pounds.

Step-by-step explanation:

The formula you are using is:

Total price * total amount= Organic price * amount organic + Rift price * amount rift

First we will simplify it by calculating it for each pound of final mix.

So this is 10.82 * 1 = 8.30 * x + 13.90 * y.

Since the total amount should be 1 pound, you could say that x+y = 1, or that y = 1-x.

If you fill this in you get

10.82 * 1 = 8.30 * x + 13.90 * (1-x)

Which you can solve as follows.

10.82 * 1 = 8.30 * x + 13.90 - 13.90x

10.82 = 13.90 - 5.6x

-5.6x = -3.08

x = -3.08/-5.6 = 0.55

So you will need 0.55 of Organic coffee for each pound of the final mix.

So in total you will need 0.55 * 80 = 44 pounds of Organic coffee.

So you need 80 - 44 = 36 pounds of Rift Valley Coffee.

To produce the desired coffee blend, the coffee distributor needs to mix approximately 51 pounds of Organic Free Trade Blend with 29 pounds of Rift Valley Blend.

This problem falls under a category of Mathematics known as Algebra. We'll start by defining two variables: x, representing the weight of the Organic Free Trade Blend, and y, representing the weight of the Rift Valley Blend.

From the total weight of the mix, we get our first equation: x + y = 80

Then, by weighing the cost of each part against the total, we get our second equation: 8.3x + 13.9y = 10.82 * 80.

Solving these two equations simultaneously, we find that approximately 51 pounds of Organic Free Trade and 29 pounds of Rift Valley blend are needed to create the desired mixture.

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Answer:

D

Step-by-step explanation:

Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.

A sequence could either be arithmetic or geometric. The truth statement about the correct student is:

Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.

Given that:

[tex]-5.5, 11, .....[/tex]

If the sequence is arithmetic, then the common difference is

[tex]d = 11 --5.5[/tex]

[tex]d = 16.5[/tex]

So, the next two elements are:

[tex]T_3 = 11 + 16.5 =27.5[/tex]

[tex]T_4 = 27.5 + 16.5 =44[/tex]

If the sequence is geometric, then the common ratio is

[tex]r =\frac{11}{-5.5}[/tex]

[tex]r= -2[/tex]

So, the next two elements are:

[tex]T_3 = 11 \times -2 = -22[/tex]

[tex]T_4 = -22 \times -2 = 44[/tex]

Based on the above computations, both students are correct.

Read more about sequence at:

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Answer:

5 12/24 -> -0.5 -> -5 6/20

Step-by-step explanation:

Negatives are lasts and positive goes first! Since the order is greatest to least.

-5 6/20 is less than -0.5 because *think of a number line -5 6/20 will be all the way to the left because it large in negative value

Answer:

4 19/32

Step-by-step explanation:

convert into improper fractions

6 1/8= 49/8

1 x 3/4= 3/4

49/8 x 3/4 = 147/32

reduce into mixed number

4 19/32

To convert the mixed numbers 6 1/8 and 1 3/4 to improper fractions, resulting in 49/8 and 7/4, respectively. Then, perform the division as multiplication with the reciprocal of the second fraction, which yields 3 1/2.

Firstly, it's essential to convert the mixed numbers into improper fractions. The given mixed numbers are 6 1/8 and 1 3/4. We can convert 6 1/8 to an improper fraction by multiplying 6 (the whole number) by 8 (the denominator) and then adding 1 (the numerator) to get 49/8. With 1 3/4, we multiply 1 (the whole number) by 4 (the denominator), then add 3 (the numerator), which gives us 7/4.

Now, the division 49/8 ÷ 7/4 can be performed. To divide fractions, we multiply the first fraction by the reciprocal of the second. Therefore, we will multiply 49/8 by 4/7. The result is 196/56. This simplifies to 3 1/2 when converted back to a mixed number.

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[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (\stackrel{x}{-6},\stackrel{y}{5})~~ \begin{cases} x=-6\\ y=5 \end{cases}\implies 5=k(-6)\implies \cfrac{5}{-6}=k~\hfill \boxed{y=-\cfrac{5}{6}x}[/tex]

Answer: 3 losses

Step-by-step explanation: The win to loss ratio is 4:1. Their losses are 1/4 of their wins. Multiply 12, their number of wins, by 1/4.

12 x 1/4 = 3

They have lost 3 games.

Given the ratio of 4:3:1 for wins, ties, and losses, and the information that the team has won 12 games, you calculate that '1 part' of the ratio equals 3 games by dividing 12 by 4. As losses are represented by '1 part' in the ratio, the team has lost 3 games.

In this baseball team scenario, the ratio of wins to ties to losses is 4:3:1 respectively. You know that the team has won 12 games. In a ratio, every part represents something equivalent, so we need to find what '1 part' is. Since '4 parts' represents 12 wins, you divide 12 by 4 to get '1 part', which is 3 games. Therefore, since losses represent '1 part' of your ratio, the team has lost 3 games.

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Answer:

Option A. The measure of angle C is 140°

Step-by-step explanation:

see the attached figure with letters to better understand the problem

we know that

The triangle OAB is an isosceles triangle

Because

OA=OB=radius

m∠BAO=m∠ABO=20°

Find the measure of angle C

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

so

m∠BAO+m∠ABO+m∠C=180°

substitute the given values

20°+20°+m∠C=180°

m∠C=180°-40°=140°