Answer:
∠ A = 56°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
2x + 3x + 40 = 180
5x + 40 = 180 ( subtract 40 from both sides )
5x = 140 ( divide both sides by 5 )
x = 28
then
∠ A = 2x = 2 × 28 = 56°
A solid glass sphere is cast with a diameter of 30 cm. find the volume of the sphere. please leave in terms of pi.
a. v = 20pie cm^3
b. v = 40pie cm^3
c. v = 4,500pie cm^3
d. v=14,137pie cm^3
Answer:
C
Step-by-step explanation:
Recall that the volume of a sphere is given by:
[tex]\displaystyle V = \frac{4}{3}\pi r^3[/tex]
Because the sphere has a diameter of 30 cm, its radius is 15 cm. Therefore, its volume is:
[tex]\displaystyle \begin{aligned} V & =\frac{4}{3}\pi(15\text{ cm})^3 \\ \\ & = \frac{4}{3}\pi(3375\text{ cm}^3) \\ \\ & = 4500\pi\text{ cm}^3 \end{aligned}[/tex]
In conclusion, our answer is C.
What is area of the figure?
Answer:
88
Step-by-step explanation:
In the figure below, lines p and q are parallel. What do you notice?
the options are alternate exterior,
alternate interior,
vertical, corresponding
and supplemantary.
What I notice about the lines p and q that are parallel is that they are both supplementary angles. Lines p and q are parallel because alternate exterior angles are congruent Lines l and m are parallel because same side interior angles are supplementary Lines l and m are parallel because alternate interior angles are supplementary
y varies inversely as x and y = 11 when x = 8. Determine the value of y when x = 16
22
5.5
17
34
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's get started ~
According to question :
[tex]\sf \dashrightarrow y \propto \dfrac{1}{x} [/tex]
[tex]\sf \dashrightarrow y = k\dfrac{1}{x} [/tex]
where, k = proportionality constantNow, we have been given that when y = 11, x = 8
Let's plug these values in equation to find value of k ~
[tex]\sf \dashrightarrow 11 = k \cdot\dfrac{1}{8} [/tex]
[tex]\sf \dashrightarrow k = 11 \times 8[/tex]
[tex]\sf \dashrightarrow k =88[/tex]
we got the value of proportionality constant. now we have been asked to find the value of y when x = 16
So, let's use the equation ~
[tex]\sf \dashrightarrow y = k \cdot\dfrac{1}{x} [/tex]
[tex]\sf \dashrightarrow y = 88\cdot\dfrac{1}{16} [/tex]
[tex]\sf \dashrightarrow y = \dfrac{11}{2} [/tex]
[tex]\sf \dashrightarrow y = 5.5[/tex]
I hope you understood the whole procedure ~
suppose that there is a circular race track. Joseph takes 25 minutes to finish it and Owuor takes 35 minutes
to finish it. If both of them start running from the same point at the same time in the same direction, after
how many minutes will they meet for the first time on the starting point?
Answer:
They will cross the finish line together in 175 minutes.
Step-by-step explanation:
This question asks you to consider the 25 and 35 times table.
I listed the 25 and 35 times tables and tried to find the lowest common multiple.
You can see that on Josephs' 7th lap of the track he will cross the line simulatneously with Owuor who will be on his 5th lap. So the answer should be 175 minutes.
25 × 1 = 25 35 × 1 = 35
25 × 2 = 50 35 × 2 = 70
25 × 3 = 75 35 × 3 = 105
25 × 4 = 100 35 × 4 = 140
25 × 5 = 125 35 × 5 = 175
25 × 6 = 150 35 × 6 = 210
25 × 7 = 175
25 × 8 = 200
The circumference of a circle is approximately 43.96 centimeters. what is the radius of the circle? use 3.14 for radius.
Answer:
7 cm
Step-by-step explanation:
The circumference of a circle is given in terms of its radius by the formula ...
C = 2πr . . . . where r represents the radius
__
Using the given values in the formula, we can find the radius to be ...
C/(2π) = r
43.96/(2×3.14) = r = 7 . . . . cm
The radius of the circle is 7 cm.
A municipal trash facility allows a person to throw away a maximum of 40 pounds of trash per week. Last week, 195 people threw away the maximum allowable trash. How many tons of trash did this equal
The total tons of trash that was thrown away by the people is 3.9 tons.
How many tons of thrash was thrown away?The first step is to convert pounds to tons
1 pound = 0.0005 tons
40 x 0.0005 = 0.02 tons
The second step is to multiply 0.02 by 195
0.02 x 195 = 3.9 tons
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your and friend got 20 frog and your friend caught 5 times more? how many did ur friend catch please explain
If you catch 3.33 frogs. Then the number of the frogs that were caught by your friend will be 16.67.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
You and your friend got 20 frogs and your friend caught 5 times more.
Let you catch x frogs. Then the number of the frogs that were caught by your friend will be 5x.
x + 5x = 20
6x = 20
x = 3.33
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Let you caught x and friend caught 5x
Now
x+5x=206x=20x=20/6x=3.335x=16.67
please please help me i will give you a ton of points
Answer:
Step-by-step explanation:
(d). V ≈ 3016
S.A. ≈ 2261
Need help please answer ASAP!
25&26
Answer:
40° and 6
Step-by-step explanation:
25. Let's suppose the angles as 2x and 7x
Then,
2x + 7x = 180°
or, 9x = 180°
or, x = 180°/9
or, x= 20°
Now, 2x is smaller
So, 2x = 2× 20° = 40°
26. Solution,
Each exterior angle = 360°\n
or, 60° = 360°/n
or, 60°n = 360 °
or, n = 360°/60°
or, n=6
As, Hexagon has 6 sides.
#26
Any polygon has sum of exterior sides as 360°
No of sides
360/60=6#25
Let the angles be 2x and 7x
2x+7x=1899x=180x=180/9x=20°Smallest angle=2(20)=40°
Pete, Lulu and Liza are walking in the Boston downtown. Each time Pete takes 4
steps, Lulu takes 3 steps. Each time Lulu takes 5 steps, Liza takes 4 steps. If Liza
takes 120 steps, how many steps does Pete take?
If Liza takes 120 steps, then the number of steps taken by Pete will be 72.
What are a ratio and a proportion?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two things are equal.
Pete, Lulu, and Liza are walking in the Boston downtown. Each time Pete takes 4 steps, Lulu takes 3 steps. Each time Lulu takes 5 steps, Liza takes 4 steps.
Then the relation between is given as
4 Pete → 4 Lulu
5 Lulu → 4 Liza
Then we have
[tex]\rm \dfrac{5}{3} \times 4 \ Pete \rightarrow \dfrac{5}{3} \ Lulu \rightarrow 4 \ Liza[/tex]
If Liza takes 120 steps, then the number of the step taken by Pete will be
[tex]\rm \dfrac{5}{3} \times 4 \ Pete \rightarrow 4 \times 120 \\\\Pete \rightarrow 72[/tex]
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Donna earns $1,404 per week at her job. However, 19% of her income gets taken out in taxes, and 12% of her income gets taken out and put into her retirement account. Which is a reasonable estimate of the amount Donna is left with each week after the money is deducted?
Answer:
About 969 dollars
Step-by-step explanation:
I kind of did it the long way. I divided $1,404 by 100 and multiplied by 19. Did the same thing with 12. Added the product of those together and subtracted from 1,404.
(1,404÷100)19 + (1,404÷100)12 = 435.24
1,404 - 435.24 = 968.76
Since it was an estimate I rounded it to the nearest whole number and got 969
Hope this helps. There are probably better methods to solve this problem but this was my way.
These points are linear. Find the slope.
Answer:
8
Step-by-step explanation:
Concepts
The formula to find the slope of a line given two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. These points represent the x- and y-coordinates of the points.
Application
To find the slope of these points, we need to take two points and use the aforementioned formula. Let's take (0, 8), and (1, 16).
Solution
[tex]\frac{(16)-(8)}{(1)-(0)}[/tex] [tex]\frac{8}{1}[/tex] [tex]8[/tex]Therefore, the slope is 8.
Answer:
slope = 8
Step-by-step explanation:
Take 2 points from the given table:
[tex]\textsf{let}\:(x_1,y_1)=(0,8)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(-1,0)[/tex]
Use the slope formula to find the slope:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-8}{-1-0}=\dfrac{-8}{-1}=8[/tex]
fully factorize
6xy-2x+3z-9zy
Answer:
(2x−3z)(3y−1)
Step-by-step explanation:
6xy-2x+3z-9zy
2x(2xy-1)+3z-9zy
2x(-1+3y)+3z(1-3y)
(2x−3z)(3y−1)
Will give Brainliest and a lot of points! :D
Which of the following expressions factors completely to 3(x + 5)²?
A. 3x² + 25
B. x² + 10x + 25
C. 3² + 75
D. 3x² + 30x + 75
Answer:
solution
here;
answer D
Step-by-step explanation:
3(x2+10x+25) 3(x^2 +2×5×x +25)3(x+5)^2PLEASE ANSWER FAST
Thirteen earthquakes were measured using the Richter scale. Their magnitudes are listed below. What is the range for this data set?
8.2, 3.1, 5.9, 2.5, 6.2, 5.1, 7.6, 9.3, 8.1, 7.4, 7.8, 6.5, 8.7
A. 6.8
B. 2.6
C. 4.1
D. 5.6
The range is found by subtracting the smallest data value from the largest data value. Here, the smallest data value is 2.5 and the largest is 9.3. Therefore, the range is:
[tex]9.3 - 2.5 = 6.8[/tex]
Therefore, the answer is Option A.
Just for extra.
The variance:1. The steps that follow are also needed for finding the standard deviation. Start by writing the computational formula for the variance of a sample:
[tex]{s^2}= \frac{{\sum}{x^2} - \frac{({\sum}{x})^2}{n}}{n-1}[/tex]
2. Create a table of 2 columns and 14 rows. There will be a header row and a row for each data value. The header row should be labeled with x and x^2. Enter the data values in the x column, with each data value in its own row. In the second column, put the square of each of the data values, x^2.
x y
8.2 67.24
3.1 9.61
5.9 34.81
2.5 6.25
6.2 38.44
5.1 26.01
7.6 57.76
9.3 86.49
8.1 65.61
7.4 54.76
7.8 60.84
6.5 42.25
8.7 75.69
3. Find the sum of all the values in the first column, [tex]{\sum}{x}[/tex].
[tex]\sum{x} = 86.4[/tex]
4. Square the answer from step 3, then divide that number by the size of the sample.
[tex]\frac{({\sum}{x})^2}{n} = \frac{7464.96}{13} = 574.22769230769[/tex]
5. Find the sum of all the values in the second column, [tex]{\sum}{x^2}[/tex].
[tex]{\sum}{x^2} = 625.76[/tex]
6. Subtract the answer in step 4 from the answer in step 5.
[tex]{\sum}{x^2} - \frac{({\sum}{x})^2}{n} = 625.76 - 574.22769230769 = 51.532307692308[/tex]
7. Divide the answer in step 6 by n - 1, one less than the size of the sample. This answer is the variance of the sample.
[tex]{s^2}= \frac{{\sum}{x^2} - \frac{({\sum}{x})^2}{n}}{n-1} = \frac{ 51.532307692308 }{12} = 4.294358974359[/tex]
Standard DeviationTo find the standard deviation, first write the computational formula for the standard deviation of the sample.
[tex]{s}= \sqrt{\frac{{\sum}{x^2} - \frac{({\sum}{x})^2}{n}}{n - 1}}[/tex]
Take the square root of the answer found in step 7 above. This number is the standard deviation of the sample. It is symbolized by [tex]s[/tex]. Here, we round the standard deviation to at most 4 decimal places.
[tex]{s} = \sqrt{4023.0714285714} = 63.4277[/tex]
A researcher determined that the heights of male students in a particular town are normally distributed
with a mean of 65 inches and a standard deviation of 1.7. Use the graph above to answer the following
questions:
a. What percentage of these students is taller than 66.7 inches?
b. If the data are based on 300 students, how many students are between 61.6 and 68.4 inches tall?
Explain.
The 16% of these students are taller than 66.7 inches and 285 students are between 61.6 and 68.4 inches tall.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
We have:
Mean of 65 inches and a standard deviation of 1.7.
From the graph:
P(X> 66.7) = (13.5 + 2.35 + 0.15)%
P(X> 66.7) = 16%
P(61.6 < X < 68.4) = (13.5 +34 + 34 + 13.5)% = 95%
= (300×95)/100
= 285 students
Thus, the 16% of these students are taller than 66.7 inches and 285 students are between 61.6 and 68.4 inches tall.
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Create and interpret tables.
ASSIGNMENT
y.=4x
Y2=422
Y3=4*
Complete the table for each function. Then
answer the questions that follow.
a=]; b=1; CE; d =
d=O
e=;f=
=
f=9=
DONE
0
0
0
1
1
4
a
b
2
С
16
d
3
e
f
g
Answer:
a = 16 b = 4 c = 8 d = 16
e = 12 f = 36 g = 64
Step-by-step explanation:
a.
Equation = [tex]y_x = 4x^{2} \\x = 1\\y_1 = 4(1)^{2} \\y_1 = 4^{2} \\y_1 = 16 \\[/tex]
b.
Equation: [tex]y_x = 4^{x} \\x = 1\\y_1 = 4^{1}\\y_1 = 4[/tex]
c.
Equation: [tex]y_x = 4x\\x = 2\\y_2 = 4(2)\\y_2 = 8[/tex]
d.
Equation: [tex]y_x = 4^{x}\\x = 2\\y_2 = 4^{2}\\y_2 = 16[/tex]
e.
Equation: [tex]y_x = 4x\\x = 3\\y_3 = 4(3)\\y_3 = 12[/tex]
f.
Equation: [tex]y_x = 4x^{2} \\x = 3\\y_3 = 4(3)^{2} \\y_3 = 4(9)\\y_3 = 36[/tex]
g.
Equation: [tex]y_x = 4^{x}\\x = 3\\y_3 = 4^{3}\\y_3 = 64[/tex]
The missing values for the function are
a= 4
b=4
c=8
d=16
e=12
f= 36
g=64
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable.
We have the table for three function.
Now, to find the following we have find the rate of change.
Function 1 : y= 4x
At x = 2 ; y= 8
At x= 3; y= 12
Function 2: y= 4x²
At x =1 ; y= 4
At x= 3; y= 36
Function 3 : y= [tex]4^x[/tex]
At x =1 ; y= 4
At x = 2 ; y= 16
At x= 3; y= 64
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A pizza has a diameter of 12in what is the Circumference
You invest $2000 compounded monthly at 9%, how much money do you have in 10 years?
Answer: The final balance is $4,734.73
In a certain Algebra 2 class of 26 students, 21 of them play basketball and 7 of them play baseball. There are 2 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answer:
Step-by-step explanation:
[tex]\frac{21}{26}*\frac{7}{26}\\ =\frac{147}{676}[/tex]
The probability of students who plays both basketball and baseball is 2/13
What is Set Theory Formula?
The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.
Given data ,
Let the number of students who plays basketball and baseball = n ( A ∩ B )
Let the number of students who plays basketball be = n ( A )
The value of n ( A ) = 21
Let the number of students who plays baseball be = n ( B )
The value of n ( B ) = 7
Now , 2 students does not play any sports out of the 26 students
So , n ( A ∪ B ) = 26 - 2
n ( A ∪ B ) = 24
Now , from the set theory formula ,
n(A∪B) = n(A) + n(B) - n(A⋂B)
Substituting the values in the equation , we get
24 = 21 + 7 - n ( A ∩ B )
Adding n ( A ∩ B ) on both sides , we get
n ( A ∩ B ) + 24 = 28
Subtracting 24 on both sides , we get
n ( A ∩ B ) = 4
So . the number of students who plays both basketball and baseball = 4
And , the probability that the student chosen plays both basketball and baseball = number of students who plays both basketball and baseball / Total number of students
Probability that the student chosen plays both basketball and baseball
= 4 / 26
= 2 / 13
Hence , The probability of students who plays both basketball and baseball is 2/13
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simplifying question
This is for AP CALCULUS. I really need help on this. I’m trying to find the first and second derivative of these three functions.
Review Material:
[tex]\sqrt[n]{x^m} = x^{\frac{m}{n}}[/tex]
[tex]\frac{d}{dx}[x^n]=nx^{n-1}\\[/tex]
[tex]\frac{d}{dx}[\sin(x)]=\cos(x)\\[/tex]
[tex]\frac{d}{dx}[\cos(x)]=-\sin(x)\\[/tex]
[tex]\frac{d}{dx}[constant]=0\\[/tex]
Step-by-step explanation:
(a)
[tex]F(x) = -2\cos(x) +x^{\frac{4}{3}} -3e\\ \text{Note: 3e is a constant}\\F'(x) = 2\sin(x) + \frac{4}{3}x^{\frac{1}{3}}\\F''(x) = 2\cos(x) + \frac{4}{9}x^{-\frac{2}{3}}[/tex]
(b)
[tex]F(x) = x^{-3} + \frac{1}{2}x^2-\sin(x)\\F'(x)=-3x^{-4} + x - \cos(x)\\F''(x) = 12x^{-5} + 1 + \sin(x)[/tex]
(c)
[tex]F(x) = 2x^{-3}+x^{\frac{3}{4}}-4x\\F'(x) = -6x^{-4} + \frac{3}{4}x^{-\frac{1}{4}}-4\\F''(x)= 24x^{-5} - \frac{3}{16}x^{-\frac{5}{4}}[/tex]
PLEASE HELP ME OUT PLEASEEEE
Answer:
I hope you know what a rectangle is, but it is true.
Step-by-step explanation:
graph of a function, f(x), has zeros at - 3, and 5. Which of
following is a factor of f(x)?
(2x - 3)
(2x + 3)
(3x + 2)
(x + 5)
The function is a quadratic function, and none of the given options is a factor of the graph of the function
How to determine the factor?The zeros of the function are given as:
-3 and 5
This means that:
x = -3 and x = 5
Rewrite as:
x + 3 = 0 and x - 5 = 0
Multiply both equations
(x + 3)(x -5) = 0 * 0
This gives
(x + 3)(x -5) = 0
Express as a function
f(x) = (x + 3)(x -5)
The above means that the factors of the function are (x + 3) and (x -5)
Hence, none of the given options is a factor of the graph of the function
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Length be x
width be x-5
So
Area=Length×Breadth
x(x-5)=750Or
If x turned y
y(y-5)=750750-y(y-5)=0Option C
Option A can be true as per commutatI've property
y²-5y=750Option B is true
Answer:
y² - 5y = 750
750 - y(y - 5) = 0
(y + 25)(y - 30) = 0
Step-by-step explanation:
Formula
Area of a rectangle = length × width
Given:
y = length of the room(y - 5) = width of the room750 ft² = area of the roomSubstituting the given values into the formula and rearranging in different way:
Equation 1
⇒ 750 = y(y - 5)
⇒ y(y - 5) = 750
⇒ y² - 5y = 750
Equation 2
⇒ 750 = y(y - 5)
⇒ 750 - y(y - 5) = 0
Equation 3
⇒ 750 = y(y - 5)
⇒ y(y - 5) - 750 = 0
⇒ y² - 5y - 750 = 0
⇒ y² - 30y + 25y - 750 = 0
⇒ y(y - 30) + 25(y - 30) = 0
⇒ (y + 25)(y - 30) = 0
pls help i beg you!
A plumber charges a flat fee of $79 to visit a home and examine a clogged drain. The plumber charges an additional $24 per hour spent fixing the drain. The total cost, C (in dollars), for fixing a drain that takes H hours is given by the following.
c=79+24h
Answer the following questions.
(a)
What is the total cost for fixing a drain that takes 7 hours?
$?
(b)
If the plumber charged a total of $343, how many hours did he spend fixing the drain?
?hours
Answer:
for "A" the answer is 247$
For "B" the answer 11 hours
Step-by-step explanation:
Malik randomly selects 60 students at Williams High School about their favorite flavor of milkshake. Of the students selected, 24 identified chocolate as their favorite milkshake. There are 1,990 students at Williams High School. Based on the data, what is the most realistic estimate for the number of students at Williams High School whose favorite ice-cream is Chocolate? A. 60 Students, B. 796 Students, C. 1,194 Students, or D. 1,400 Students?
Answer:
B
Step-by-step explanation:
The answer is B as this is a simple ration question.
All you need to do is convert the question into ration fraction form:
24/60 =x/1990
x is the number of people whose favourite ice-cream is chocolate.
Do cross multiply on both sides and you will get 47760=60x.
x= 796.
Thus, you get your answer.
If h(x) = |2x−6| -2, then what is h(-1)
Answer:
[tex]h(-1)[/tex] ⇢ [tex]-h[/tex]
Please solve this for me