5. Solve the logarithmic equation by writing in exponential form or by graphing. Round to the nearest
log (3x + 1) = 2
0.667
33.667
33
0.333

Answer:

a) 80
b) 56

Step-by-step explanation:

a) Calculate the volume of the the cup using volume of cylinder equation: [tex]V = \pi r^{2} h[/tex]

Where V = Volume, r=radius, and h=height. Your answer should be in cubic inches ([tex]in^3[/tex]).
You're given diameter, so use equation [tex]d/2 = r[/tex] to find radius.
Substituting these equations will give you: [tex]V = \pi (d/2)^2 h[/tex]
However, the given volume of the sink is 3000[tex]\pi[/tex], meaning that you should modify your results to match this value. Do not substitute [tex]\pi[/tex] for 3.14..., leave it as a symbolic value. Your final V of the cup should = 37.5 [tex]\pi[/tex]
Divide the volume of the sink by the volume of the cup. This number will be the amount of cups needed to empty it. In equation form:
[tex]Vsink / V cup =[/tex] # of cups.
Note the the [tex]\pi[/tex] will cancel each other out, so there's not need to factor that in.
b) Repeat the steps above with the new d (diameter) value.

Answer:

a) 117.75

Step-by-step explanation:

3.14 * 2.5^2=19.625

19.625*6=117.75

The area of the irregular polygon = area of the 2 triangles + area of the rectangle = 25 units².

The irregular polygon can be decomposed into two triangles and a rectangle.

Area of triangle AGE = ½bh = ½(6)(3) = 9 units²

Area of triangle EGF = ½bh = ½(2)(4) = 4 units²

Area of rectangle ABCD = (length)(width) = (4)(3) = 12 units²

Area of the irregular polygon = 9 + 4 + 12 = 25 units².

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Answer:

the answer is 720

Step-by-step explanation:

I took the test

Answer:

  (a)  46°

  (b)  86°

Step-by-step explanation:

When the secants cross externally (figure a), the angle where they cross is half the difference of the subtended arcs.

When they cross internally (figure b), the angle is half the sum of the subtended arcs.

__

Half the difference of arcs VW and VX is ...

  ∠VYW = 1/2(160° -68°) = 46°

  m∠VYW = 46°

__

Half the sum of arcs AB and CD is ...

  ∠CED = 1/2(arc AB +arc CD)

  2×∠CED = arc AB +arc CD . . . . . multiply by 2

  2×∠CED -arc AB = arc CD . . . . . subtract arc AB

  arc CD = 2×85° -84° = 86°

  m arc CD = 86°

Answer:

when you are comparing two sets of data, and one set is strongly skewed and the other is symmetric, which measures of the center and variation should you choose for the comparison?

Step-by-step explanation:

The unit circle is a circle in the form of

[tex] {x}^{2} + {y}^{2} = 1[/tex]

while x = cos t

y= sin t

, where t is an angle

So we plug in -1/7, for x to find y

[tex]( \frac{ - 1}{7} ) {}^{2} + {y}^{2} = 1[/tex]

[tex] {y}^{2} = \frac{49}{49} - \frac{1}{49} [/tex]

[tex]y = \frac{4 \sqrt{3} }{7} [/tex]

If the point is in the 2nd quadrant, your value of y is positive

If it in the third quadrant, the y value is negative

Answer:

9.9

Step-by-step explanation:

Volume of cube= side x side x side = (side)³

(side)³ = 979

= side = ∛979

= 9.9

Answer:

128

Step-by-step explanation:

There are 2 lengths, 16 x 2 = 32. 48 - 32 = 16. 16 divded by 2 equals 8. 8 x 16 = 128.

The line plot shown in the graph as 25 repeated 1 time, 25 1/2 repeated 2 times and so on.

A line graph is a graph made up of segments of straight lines that connect the depicted data points.

Draw dots on each of the data element in the data set:

25 repeated 1 time

25 1/2 repeated 2 times

26 repeated 1 time

27 3/4 repeated 1 time

and so on.

Thus, the line plot shown in the graph as 25 repeated 1 time, 25 1/2 repeated 2 times and so on.

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To add more answer options, click the + Add an answer button below the answer options A and B. You can add up to 10 answer options in total for a multiple choice question. Indicate the correct answer(s) using the checkbox(es) aligned to the right of the answer options

Answer:

[tex]\angle{EBC}=35\textdegree[/tex]

An angle bisector divides the angle measure into two equal parts. In triangle ABC, B is the point at which the angle lies.

Step-by-step explanation:

Picture segment BD drawn from point B of tri.ABC where it connects to segment AC, creating point D. Now picture E drawn on the newly created segment DC where it connects to point B and down to point C. Here's a drawing to better show this:

It's bisecting the bisected angle ABC. So, 140/2 = 70, and 70/2 = 35.

The amount of dollars that Ms. Duran would have at the end of the day if she started the day with $0 is 665 dollars.

The value of the account will increase when she receives her pay check and wine the lotto earnings. The value of the account would decrease when she pay for gasoline, groceries and phone bill.

Balance = 895 - 95 - 129 - 84 + 78 = 665 dollars

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Answer:

4.5 hours

Step-by-step explanation:

If 2 miles takes 1.5 hours, then 6 miles will be 4.5 hours.

2 miles = 1.5 hours

6 times 1.5 = 4.5

Therefore, 6 miles will take 4.5 hours.

Answer:

4.5 Hours

Step-by-step explanation:

2/1.5=6/ x

Cross multiply

2x=1.5*6

2x=9

x=4.5

Answer:

A and C.

Step-by-step explanation:

We are given that: "The square of a number (which we can call x) is three less than four times the number."

In other words:

[tex]\displaystyle x^2 = 4x - 3[/tex]

Hence solve for x by isolating the equation and factoring:

[tex]\displaystyle \begin{aligned} x^2 - 4x + 3 & = 0 \\ \\ (x-1)(x-3) & = 0 \\ \\ x & = 1 \text{ or } x = 3 \end{aligned}[/tex]

In conclusion, our answers are A and C.

Answer: 5/6

Step-by-step explanation:

5/8 / 3/4

5/8 * 4/3= 20/24

20/24 / 4/4 = 5/6

Answer:

Average per floor = 162 dollars.

Step-by-step explanation:

Remark

First find the number of floors

Then make a total   income received from those floors.

Then divide the total income by the number of floors, to get the average

Number of floors

Total number of floors = 6 + 2 + 1 = 9 floors

Total income

Total income = cost per floor * the number of floors.

Total income

6 * 140 =  840

2 * 220 = 440

1 * 178   = 178

Total    = 1458

Average income / Floor

Average income / Floor = Total amount / number of floors

Average Income / Floor = 1458 / 9 =  162

Answer:

B. photographs

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

I hope this helps! If it does, please mark me Brainliest! Thanks in advance!

Answer:

C.  16 : 22

Step-by-step explanation:

Given:

Ratio of apples trees to orange trees:

⇒ apple : orange

⇒ 16 : 22

Answer:

0.91666666666 hope this helps

just literally divide

The constant sum for the ellipse with the foci (-5,5) and (0,7) and the point (0,5) is 7

The foci of the ellipse are given as:

F1(−5, 5) aF2(0, 7)

The point is then given as:

Point (0, 5)

Calculate the distance between each focus and the point using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

So, we have:

[tex]F_1 = \sqrt{(-5-0)^2 + (5-5)^2}[/tex]

Evaluate

[tex]F_1 = 5[/tex]

Also, we have:

[tex]F_2 = \sqrt{(0-0)^2 + (7-5)^2}[/tex]

Evaluate

[tex]F_2 = 2\\[/tex]

The constant sum is then calculated using:

Constant sum = F1 + F2

So, we have:

Constant sum = 5 + 2

Evaluate

Constant sum = 7

Hence, the constant sum is 7

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The solution to the question is [tex]\rm 16\dfrac{1}{2}[/tex] .

Whole numbers is a collection of all the basic counting numbers and 0. In mathematics, counting numbers are called natural numbers.

So, we can define the whole number as a collection of all natural numbers and 0. Whole numbers also include all positive integers along with zero.

A proper fraction is a fraction whose numerator is smaller than its denominator.

An improper fraction is a fraction whose numerator is equal to or greater than its denominator.

The given question is [tex]\rm 6\dfrac{3}{4} + 4\dfrac{2}{4} +5\dfrac{1}{4}[/tex]

this can be also written as

[tex]\rm \dfrac{27}{4} +\dfrac{18}{4} +\dfrac{21}{4}[/tex]

as they have same bases

[tex]\rm \dfrac{66}{4}\\\\\\\dfrac{33}{2}\\\\16\dfrac{1}{2}[/tex]

Therefore this is the solution.

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Hello..!

If you say that the value of x is an integer then the number when divided by 3 which is "3x" will result in an integer:

[tex]{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \sf40 \div 3 = 13.33}}[/tex]

Option A) does NOT return an integer so it is not the answer.

[tex]{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \sf41 \div 3 = 13.66}}[/tex]

Option B) is also not the answer.

[tex]{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \sf42 \div 3 = 14}}[/tex]

Option C) does result in an integer but let's see the others:

[tex]{\: \: \: \: \: \: \: \: \: \: \: \: \: \: { \sf{43 \div 3 = 14.33}}}[/tex]

Option D) also does not return an integer.

[tex]{\: \: \: \: \: \: \: \: \: \: \: \: \: \sf{44 \div 3 = 14.66}}[/tex]

And lastly option E) does not result in an integer so the only one that results in an integer is option C) and that is the 42nd answer.

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf{\sf \orange\longmapsto{ \red{C) \: \green{42°} }}}[/tex]

So, the correct part is C)42°

Answer:

The result is

Hope this helped

Answer:

yes

Step-by-step explanation:

you have to use trigonometry to find the area of a parallelogram without the height.

the formula is: Area = ab(sin(x))

Where a and b are the length of parallel sides and x is the angle between the sides of the parallelogram.

Answer:

0.0102 g

Step-by-step explanation: A common formula for determining the amount of sample remaining in terms of its half-life is

where

t = 50 000 yr

      Calculate n

n = 50 000/5730

n = 8.726

N₀ = 4.30 g                       Calculate N

N = 4.30 × 2.36 × 10⁻³

N₀ = 0.0102 g please mark me brainliest

Answer:

  0.0102 g

Step-by-step explanation:

You want to know the amount of C-14 remaining in a tree branch after 50,000 years if it originally had 4.30 grams, and C-14 has a half-life of 5730 years.

The number of grams (N) remaining is given by the formula ...

  N = N₀(1/2)^(t/5370)

where t is the number of years and N₀ is the initial amount of C-14.

The amount of C-14 remaining in the tree branch will be ...

  N = 4.30×(1/2)^(50000/5730) ≈ 0.010154 . . . . grams

This can be rounded several ways, depending on the criterion you choose.

The initial value 4.30 has 3 significant figures, so this could be rounded to 3 significant figures as 0.0102 g. This is the value we show at the top of this answer.

The initial value is accurate to a hundredth of a gram, so this could be rounded to a hundredth of a gram as 0.01 g.

The value 50,000 years has 1 significant digit, so we could round this to 1 significant digit as 0.01 g.

__

Additional comment

The problem statement gives the initial amount twice, once with 3 significant figures, and once with only 2 significant figures. If the answer is rounded to 2 significant figures, it would be 0.010 g.

There does not appear to be any justification for an answer of 0.0100 grams.

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Answer:

[tex]t_n=n[/tex]

Step-by-step explanation:

Arithmetic sequence

General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]

where:

Given sequence: 1, 2, 3, 4, 5, ...

Therefore:

Substituting the given values into the formula:

[tex]\implies t_n=1+(n-1)1[/tex]

[tex]\implies t_n=1+n-1[/tex]

[tex]\implies t_n=n[/tex]

Therefore, [tex]t_n=n[/tex]

Answer:

225.5 sq. mm

Step-by-step explanation:

triangle:5x(9+4+4+4)=15x21÷2=157.5

5x(4+4)=5x8=40

7x4=28

157.5+40+28=157.5+68=225.5

Answer:

153.86 ft squared

Step-by-step explanation:

A = πr^2
A = 3.14(7)^2
A = 3.14*49
A = 153.86

Hope this helps, good luck on the test!

Answer:

116

Step-by-step explanation:

290% as a decimal is 2.9. "Of" means multiply. You can now multiply 2.9 by 40 to get the answer 116.