Answer:
7.04 trillion = 7.04 x 10¹²
Step-by-step explanation:
Answer: 7.04 x 10^12
Step-by-step explanation:
Just took the test :)
help me with this please
Answer:
m∠8 = 124°
Step-by-step explanation:
1. Find m∠1
m∠1 and m∠2 are supplementary, since they are on the same line.
That means m∠1 + m∠2 = 180.
Plug in: 4x + 2x - 6 = 180
Simplify + subtract: 6x = 186
Divide: x = 31
Plug in: m∠1 = 4(31) --> m∠1 = 124°
2. Since ∠1 and ∠4 are vertical, they are congruent. Since ∠4 and ∠8 are corresponding on parallel lines, they are also congruent. Therefore, ∠1 and ∠8 are congruent, which means m∠1 = m∠8
Plug in: m∠8 = 124°
Based on these results, if 250 children are asked about their favorite activity, how many children will prefer organize sports?
Answer:
60 out of 250 children will prefer organized sports.
Step-by-step explanation:
We are given the results of a random survey of children between the ages of 13 and 18 about their favorite activity.
Based on these results, we are to find the number of children who will prefer organized sports if 250 children were asked about their favorite activity.
Children who will prefer organized sports = [tex]\frac{37}{155} \times 250[/tex] = 60
Cade made A table to relate two units of time. The number pairs in his Table are One and 24, two and 48, three and 72, four and 96. What are the best labels for Cades table
Answer:
Days, Hours
Step-by-step explanation:
1 day = 24 hours
2 days = 48 hours
3 days = 72 hours
4 days = 96 hours
(its increasing by 24)
Write x^3/2 in radical form
Answer:
Step-by-step explanation:
I think you meant x^(3/2). This breaks down in at least two ways:
[x^3]^(1/2), or √(x^3)m or √x³), or
[x^(1/2)]^3 = (√x)^3
To write [tex]x^{3/2}[/tex] in radical form, rewrite it as (√x)³or √(x³). This utilizes the relationship between fractional exponents and radicals.
To write [tex]x^{3/2}[/tex] in radical form, we can use the relationship between exponents and radicals. In general, the expression [tex]x^{a/b}[/tex] can be written in radical form as the b-th root of x raised to the power 'a'. So, applying this rule to the given expression.
[tex]x^{3/2}[/tex]
Step-by-Step Explanation:
Rewrite the exponent 3/2 as a fraction where the numerator is the power and the denominator is the index of the root.So, [tex]x^{3/2}[/tex] can be written as the square root of x raised to the power of 3.This translates to: (√x)³ or equivalently, [tex](x^{3})^{1/2}[/tex] which means the square root of x cubed.Therefore, the radical form of [tex]x^{3/2}[/tex] is √x³ or (√x)³.
I NEED HELP PLEASE !
A big ship drops its anchor.
E(t) models the anchor's elevation relative to the water's surface (in meters) as a function of time t (in seconds)
E (t) = -2.4t + 75
How far does the anchor drop every 5 seconds?
Answer:
The answer is 75
Step-by-step explanation:
Find m
Answers choices
53
44
65
35
For this case we have to define trigonometric relations of rectangular triangles that:
The cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle.The sine of an angle is given by the leg opposite the angle on the hypotenuse of the triangle.Then, according to the figure we have:
[tex]Sin (M) = \frac {3} {5}\\M = ArcSine (\frac {3} {5})[/tex]
[tex]M = 36.87[/tex] degrees
Answer:
36.87 degrees
Ice cream beans are selling for $10 per pound and durians are selling for $9 per pound. If the market sold a total of $196 worth of durians and ice cream beans yesterday, and it sold 11 pounds of durian, which of the following is a good estimation of the total pounds of ice cream beans sold?
.
Durain beans cost $9 per pound and they sold 11 pounds.
Multiply the cost by the amount sold: 9 x 11 = $99
Subtract that from the total sold:
196 - 99 = $97
Now divide the amount left by the cost per pound for Ice cream beans:
97 / 10 = 9.7 pounds.
Round the answer as needed to match one of your choices.
Is x+2=14 a one-step or two-step equation?
This is just a ONE STEP equation.
It is, because all you must do to solve for "x" is subtract 2
Answer:
one-step equation
x+2=14
x+2-2=14-2
x=12
A circle with area 81 has a sector with a central angle of 120 what is the area of the sector
Answer:
27
Step-by-step explanation:
The central angle of 120° is 1/3 of the entire circle of 360°, so the sector area is 1/3 of the circle area:
1/3×81 = 27
The sector area is 27.
15 points please answer asap
The answer is:
The area of this figure is 946 square inches.
Why?We can see that the figure is composed by two rectangles with diferrent dimensions, so, to calculate the area of the entire figure.
So,
For the first rectangle, we have:
[tex]Base=7in\\Height=28in[/tex]
The area will be:
[tex]Area=Base*Height=7in*28in=196in^{2}[/tex]
For the second rectangle, we have:
[tex]Base=25in\\Height=30in[/tex]
The area will be:
[tex]Area=Base*Height=30in*25in=750in^{2}[/tex]
Now, calculating the area of the entire figure, we have:
[tex]TotalArea=FirstRectangleArea+SecondRectangleArea\\\\TotalArea=196in^{2}+750in^{2}=946in^{2}[/tex]
Have a nice day!
What is the simplified expression for the expression below?
Answer:
3x+5
Step-by-step explanation:
i took test
The initial number of carbon-14 atoms in the organism at death is
The initial number of carbon-14 atoms in the organism at the time of death was 200 atoms.
The initial number of carbon-14 atoms in the organism at death can be calculated using the formula for exponential decay:
[tex]\[ N(t) = N_0 e^{-\lambda t} \][/tex]
where:
- [tex]\( N(t) \)[/tex] is the number of undecayed carbon-14 atoms at time [tex]\( t \),[/tex]
- [tex]\( N_0 \)[/tex] is the initial number of carbon-14 atoms at time \[tex]( t = 0 \[/tex]) (the time of death),
- [tex]\( \lambda \)[/tex] is the decay constant for carbon-14,
- [tex]\( t \)[/tex] is the time that has passed since the time of death.
Given that after 5730 years (the half-life of carbon-14), the number of undecayed carbon-14 atoms is half the initial amount, we can write:
[tex]\[ \frac{N_0}{2} = N_0 e^{-\lambda \times 5730} \][/tex]
To find the decay constant [tex]\( \lambda \)[/tex], we use the half-life formula:
[tex]\[ \lambda = \frac{\ln(2)}{t_{1/2}} \][/tex]
where [tex]\( t_{1/2} \)[/tex] is the half-life of carbon-14, which is 5730 years. Plugging in the values:
[tex]\[ \lambda = \frac{\ln(2)}{5730} \][/tex]
Now, we can solve for [tex]\( N_0 \)[/tex]using the information provided:
[tex]\[ 100 = N_0 e^{-\frac{\ln(2)}{5730} \times 573[/tex]
Since [tex]\( e^{-\ln(2)} = \frac{1}{2} \)[/tex], the equation simplifies to:
[tex]\[ 100 = N_0 \times \frac{1}{2} \][/tex]
Solving for [tex]\( N_0 \):[/tex]
[tex]\[ N_0 = 100 \times 2 \][/tex]
[tex]\[ N_0 = 200 \][/tex]
Therefore, the initial number of carbon-14 atoms in the organism at the time of death was 200 atoms.
which point lies outside the circle with equation (x - 2) + (y + 3) = 4 (1, -4 ) ( 0, -3 ) ( 2, 0 ) (2, -4 )
Answer:
The point (2,0) is outside the circle
Step-by-step explanation:
we have
[tex](x-2)^{2}+(y+3)^{2}=4[/tex]
[tex](x-2)^{2}+(y+3)^{2}=2^{2}[/tex]
This is the equation of a circle with center at (2,-3) and radius equal to 2 units
Using a graphing tool
Plot the circle and the given points and verify if the point lie outside the circle
we have
[tex](1, -4 ),(0, -3),(2, 0),(2,-4)[/tex]
so
The point (2,0) is outside the circle
see the attached figure
What is the distance between points (7, -4) and (7, 9)?
Answer:
13Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (7, -4) and (7, 9). Substitute:
[tex]d=\sqrt{(7-7)^2+(9-(-4))^2}=\sqrt{0+13^2}=\sqrt{13^2}=13[/tex]
Used [tex]\sqrt{a^2}=a[/tex]
Which shapes can the composite figure be divided into to find the area?
a rectangle and a triangle
a rectangle and two triangles
a trapezoid and a rectangle
a trapezoid and two triangles
Answer:
a rectangle with two triangles.
Step-by-step explanation:
this way you will be able to find the area of the rectangle then add it to the area of the two triangles.
Answer:
the correct answer is b
Step-by-step explanation:
A standard deck has 52 cards, and contains 13 cards of each of the four suites: diamonds, spades, hearts, and clubs. What is the probability that you choose a diamond, given that you have already chosen a diamond and have not replaced it?
a) 1/4
b) 13/51
c) 3/13
d) 4/17
Answer:
Option d) [tex]P=\frac{4}{17}[/tex]
Step-by-step explanation:
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
so
Let
x------> size of the event space
y-----> size of the sample space
so
[tex]P=\frac{x}{y}[/tex]
In this problem we have
[tex]x=13-1=12[/tex]
[tex]y=52-1=51[/tex]
substitute
[tex]P=\frac{12}{51}[/tex]
Simplify
[tex]P=\frac{4}{17}[/tex]
Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a
factor of k, where k>0.
(a) Are Rectangle 1 and Rectangle 2 similar? Why or why not?
(b) Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.
(c) Write a paragraph proof to show that the area of Rectangle 2 is k2 times the area of Rectangle 1.
Answer:
a) yes they are similar
b)Proved below
c)Proved below
Step-by-step explanation:
a) rectangle 1 and 2 are similar by definition of similar rectangles.
Definition of similar rectangles states that two rectangles are similar if they have same shape but different sizes. The ratio between their corresponding sides are same, in this case as rectangle 2 is made by multiplying each dimension of Rectangle 1 by a
factor of k, where k>0 thus providing same proportion in length of different corresponding sides of two rectangles hence rectangle 1 and 2 are similar.
b) Perimeter of rectangle 1, P1= s1+ s2+ s3 + s4
As each side of rectangle 2 is formed by multiplying each dimension of Rectangle 1 by k, therefore
Perimeter of rectangle 2, P2= k.s1+ k.s2+ k.s3 + k.s4
Taking k common
= k(s1+ s2+ s3 + s4)
Substituting P1 in above expression
P2 =k(P1)
Hence the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.
c) Area of rectangle 1, A1= 2(s1)(s2)
As each side of rectangle 2 is formed by multiplying each dimension of Rectangle 1 by k, therefore
Area of rectangle 2, A2= 2(k.s1)(k.s2)
= 2k^2(s1)(s2)
= k^2 [2(s1)(s2)]
Substituting A1 in above expression
A2 = k^2(A1)
Hence the area of Rectangle 2 is k2 times the area of Rectangle 1 !
State your variables and what they represent. Write a linear function describing the situation. Use the function to solve the problem.
A phone costs $8 per month, plus 10 cents per message unit. How much is the monthly bill if 40 message units are used?
Answer:
y = 0.10x + 8, $12
Step-by-step explanation:
y = monthly bill
x = number of message units
Each message unit costs $0.10, so the cost of x message units is 0.10x. The phone adds $8 to the monthly bill. Therefore:
y = 0.10x + 8
If x = 40, then:
y = 0.10 (40) + 8
y = 4 + 8
y = 12
The monthly bill is $12.
I need help please????
Answer:
x = - 1
Step-by-step explanation:
Given
3x + 2 = y and y = - 1
Substitute y = - 1 into the equation and solve for x, that is
3x + 2 = - 1 ( subtract 2 from both sides )
3x = - 3 ( divide both sides by 3 )
x = - 1
This is verified by the point on the graph with coordinates (- 1, - 1)
Method 1: By substitution
Step 1: In the equation 3x + 2 = y when you see a y replace it with -1
3x + 2 = -1
Step 2: Combine like terms by subtracting 2 to both sides
3x + (2-2) = -1 - 2
3x = -3
Step 3: Isolate x by dividing 3 to both sides
[tex]\frac{3x}{3} = \frac{-3}{3}[/tex]
x = -1
Method 2: By looking at the graph
To solve this way you see where the line on the graph has y = -1 and look for its complimentary x
If you look at the graph attached below you can see that at y = -1 the x also equals -1
x = -1
Hope this helped!
30 points, Please help with trig
X is 4 and Y is 4 Square Root of 2 (or 5.656854)
Find f/g for the functions provided. 10 points Help needed.
ANSWER
[tex]( \frac{f}{g} )(x) = \frac{1}{3} ( {x}^{2} + 3x + 9)[/tex]
EXPLANATION
The given functions are
[tex]f(x) = {x}^{3} - 27[/tex]
and
[tex]g(x) = 3x - 9[/tex]
[tex]( \frac{f}{g} )(x) = \frac{f(x)}{g(x)} [/tex]
[tex]( \frac{f}{g} )(x) = \frac{ {x}^{3} - 27}{3x - 9} [/tex]
[tex]( \frac{f}{g} )(x) = \frac{ (x - 3)( {x}^{2} + 3x + 9) }{3(x -3 )} [/tex]
Cancel the common factors,
[tex]( \frac{f}{g} )(x) = \frac{ {x}^{2} + 3x + 9 }{3} [/tex]
OR
[tex]( \frac{f}{g} )(x) = \frac{1}{3} ( {x}^{2} + 3x + 9)[/tex]
Bethany added a decorative border across the top of each wall of her kitchen. A diagram of her kitchen is shown below.
She used a total of 62 feet of border. What is the length in feet of the unlabeled wall?
Choices:
a.) 5
b.) 10
c.) 8
d.) 13
The answer is your mom. Nah it’s B)10
For this case we have that the perimeter of the figure is given by the sum of its sides, they tell us that the perimeter is 62 feet.
So:
Let "x" be the variable that represents the length of the unlabeled wall, so the perimeter is:
[tex]x + 8 + 5 + 13 + 18 + 8 = 62[/tex]
We find the value of "x":
[tex]x = 62-8-5-13-18-8\\x = 10[/tex]
Thus, the length of the unlabeled wall is 10 feet.
Answer:
Option B
What is 37.5% as a fraction
37.5% as a fraction is 3/8.
Answer:
3/8
Step-by-step explanation:
To write a percent as a fraction, divide the percent by 100.
37.5% = 37.5/100
Now we reduce the fraction. First, multiply the numerator and denominator by 2 to get rid of the decimal in the numerator.
37.5% = 37.5/100 = 75/200
Both the numerator and denominator are divisible by 5, so we divide them by 5.
37.5% = 37.5/100 = 75/200 = 15/40
Both the numerator and denominator are divisible by 5 again, so we divide them by 5 again.
37.5% = 37.5/100 = 75/200 = 15/40 = 3/8
Answer: 37.5% = 3/8
2 pounds equals how many onces
There are 16 oz in a pound, so 2 lbs is 32 oz.
Answer: two pounds is equivalent to 32 ounces.
Step-by-step explanation: 1 pound is equal to 16 ounces, and since 2 is 1 two times, just multiply 16 by 2, 16x2=32 ounces
Will mark BRAINLIEST!
Hello There!
The first one seems alright.
The second one it would be 1/2.
This is because half of the options have “R” on them.
Answer: 1. is 5/6
2. is 1/2
Step-by-step explanation:
Explain how to determine the number of square feet required to cover your rectangular garden that has a length of 10 feet and a width of 8 feet?
Answer:
Multiply the length and the width of the shape together to get the area of the square or rectangle in square feet.
10 multiplied by 8 equals 80 square feet
Step-by-step explanation:
Got a 100 on it.
Final answer:
To cover a rectangular garden measuring 10 feet by 8 feet, multiply the length by the width to get an area of 80 square feet, which is the amount of material needed.
Explanation:
Calculating the Area of a Rectangular Garden
To determine the number of square feet required to cover your rectangular garden, you need to calculate the area of the garden. The area of a rectangle is found by multiplying the length by the width. In this case, the garden has a length of 10 feet and a width of 8 feet.
Steps to Calculate the Area
Measure the length and width of the garden using a measuring tape.
Multiply the length by the width to get the area in square feet: 10 feet (length) × 8 feet (width) = 80 square feet.
Therefore, you would need 80 square feet of material to cover the entire garden.
Least to greatest 3/10, 0.222, 3/5, 0.53
The answer is .22222..., 3/10, .53, and 3/5.
Hope this helps!
Hello there!
The numbers in order from least to greatest are:
0.2222, 3/10, 0.53, 3/5
Start by turning all the numbers into either decimals. To do this, take the two fractions, 3/5 and 3/10 and divide them out.
3 divided by 5 = 0.6
3 divided by 10 = 0.3
Now let's look at our numbers again.
0.3, 0.222, 0.6, 0.53.
We know that 2 is less than 3, and 3 is less than 5, and 5 is less than 6, so lets rearrange the numbers into that order.
0.2222, 0.3, 0.53, 0.6
Now, convert any fractions that were converted into decimals back into their original forms.
0.2222, 3/10, 0.53, 3/5
This is your final answer. I hope this helps and have a great day!
what is the remainder in the synthetic division problem
Answer:
C
Step-by-step explanation:
1 | 4 6 - 2
4 10
------------------
4 10 8 ← remainder
Answer:
Option C
Step-by-step explanation:
Given is a division in synthetic
We have to find the remainder
The divisor is x-1 and dividend is [tex]4x^2+6x-2[/tex]
By synthetic division we get the following:
1) 4 6 -2\\
4 10\\
----------------------\\
4 10 8=R
Thus remainder is 8
The sixth grade chorus has a boy to girl ratio of 3:8 which of the following ratios is equivalent to this ratio?
A) 15 boys to 55 girls
B) 55 boys to 15 girls
C) 40 boys to 15 girls
D) 15 boys to 40 girls
The ratio in option (D), 15 boys to 40 girls is equivalent to 3 : 8.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
The given ratio of boy to girls is 3 : 8.
To find the equivalent ratio to 3:8.
Solve with the help of option,
(A)
15 boys to 55 girls.
The ratio 15 : 55 = 3 : 11
(B)
55 boys to 15 girls,
The ratio 55 : 15 = 11 : 3.
(C)
40 boys to 15 girls,
The ratio 40 : 15 = 8 : 3
(D)
15 boys to 40 girls,
The ratio 15 : 40 = 3 : 8.
The ratio of 15 boys to 40 girls is 3:8.
Hence, the correct option is (D).
To learn more about Ratio on :
https://brainly.com/question/13419413
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What is (1-7x)(1+9x)
ANSWER
[tex](1-7x)(1+9x) =- 63 {x}^{2} + 2x + 1[/tex]
EXPLANATION
The given product is (1-7x)(1+9x).
Expand using the distributive property.
[tex](1-7x)(1+9x) = 1(1 + 9x) - 7x(1 + 9x)[/tex]
[tex](1-7x)(1+9x) = 1 + 9x - 7x - 63 {x}^{2}[/tex]
Simplify to obtain:
[tex](1-7x)(1+9x) = 1 + 2x - 63 {x}^{2}[/tex]
You can rewrite in standard form to get,
[tex](1-7x)(1+9x) =- 63 {x}^{2} + 2x + 1[/tex]
Answer:
1+2x-63x^2
Step-by-step explanation:
factor 1(1+9x)=1+9X
-7x(1+9x)=-7x-63x^2
add 1+9x-7x-63x2