Answer:
d) the height of red prism is three times the height of the blue prism.
Step-by-step explanation:
i) the volume of a rectangular prism is given by area of base [tex]\times[/tex] height.
ii) volume of the blue prism is = (base of blue prism) [tex]\times[/tex] (height of blue prism)
iii) volume of red prism is = (base of red prism) [tex]\times[/tex] ( height of the red prism)
= [tex]\frac{1}{3}[/tex] [tex]\times[/tex] ( base of blue prism) [tex]\height[/tex][tex]\times[/tex] ( height of red prism)
iv) it is also given that
volume of blue prism = volume of red prism
⇒ (base of blue prism) [tex]\times[/tex] (height of blue prism) = (base of red prism)[tex]\times[/tex] (height of red prism)
⇒(base of blue prism) [tex]\times[/tex] (height of blue prism) = [tex]\frac{1}{3}[/tex] [tex]\times[/tex] ( base of blue prism)[tex]\times[/tex] (height of red prism)
⇒ (height of blue prism) = [tex]\frac{1}{3}[/tex] [tex]\times[/tex] (height of red prism)
∴ height of red prism = 3 [tex]\times[/tex] height of blue prism
Therefore the correct option is
d) the height of red prism is three times the height of the blue prism.
Write the name of each angle arm
A to O to C
Answer:
∠AOC
Step-by-step explanation:
The statement "A to O to C" is talking about each of the points that form an angle. Each point is given a letter as its name.
The symbol ∠ means angle.
You need two lines to form an angle, and you need two points to form a line. By reusing one of the points, you need three points to form an angle. The point that is being reused is always the point in the middle, in this case, that point is called 'O'.
Evaluate [ sin^2 -(cos^2@)(sin^2)]^-1 for @=30 degrees. The value of this expression is
Answer:
Step-by-step explanation:
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.
− sin ( π 2 )
The exact value of sin ( π 2 ) is 1 .
-1.1
Multiply
− 1 by 1 .
−1
SIN (3 PIE/2)
Cindy’s apartment complex is offering renters insurance through their insurance company. The insurance company charges an annual premium of $565.00 which can be paid in equal payments throughout the year with her monthly rent. Cindys monthly rent is currently $789.00. What will Cindy's new rent be if she includes the renters insurance
Answer:
C: $836.08
Step-by-step explanation:
Edg 2020
The Cindy's new rent be if she includes the renters insurance is $836.08
We are given that;
An annual premium = $565.00
Now,
To find Cindy's new rent, we need to add the monthly payment for the renters insurance to her current rent.
To find the monthly payment for the insurance, we need to divide the annual premium by 12, since there are 12 months in a year. We get:
565 / 12 = 47.08
So, the monthly payment for the insurance is $47.08.
Adding this to Cindy's current rent, we get:
789 + 47.08 = 836.08
Therefore, by unitary method the answer will be $836.08.
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At bright minds learning , 75% of employees work as instructors . If there are 300 employees at bright mind Learning , how many of them work as instructors ?
Answer:
225 employees work as instructors.
Step-by-step explanation:
You want to find what 75% OF 300 is, therefore multiplication will be required in this problem. First you want to convert 75% to a decimal which you could do by just bringing the decimal point to the left twice. which will give you the decimal 0.75.
Now multiply. 0.75*300=225. There are 225 employees that work as instructors.
Final answer:
To find out how many employees work as instructors at Bright Mind Learning, multiply 75% by the total number of employees. 225 of the 300 employees at Bright Mind Learning work as instructors.
Explanation:
To find out how many employees work as instructors at Bright Mind Learning, we need to calculate 75% of the total number of employees. First, convert 75% to a decimal by dividing it by 100: 75/100 = 0.75. Then, multiply this decimal by the total number of employees (300): 0.75 * 300 = 225.
So, 225 of the 300 employees at Bright Mind Learning work as instructors.
Find the slope of the line that passed though the two points
(0,5) and (-9, -4)
To find the slope, use the slope(m) formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and plug in the two points
(0, 5) = (x₁, y₁)
(-9, -4) = (x₂, y₂)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-4-5}{-9-0}[/tex]
[tex]m=\frac{-9}{-9}[/tex] [two negatives cancel each other out and become positive]
m = 1 The slope is 1
azmin is completing an art project. She has two pieces of construction paper. The first piece is 44 cm wide and the second piece is 33 cm wide. Jazmin wants to cut the paper into strips that are equal in width and are as wide as possible. How wide should Jazmin cut each strip?
Answer:
11 cm
Step-by-step explanation:
Answer:
is there a picture
Step-by-step explanation:
Jeremy has a deck of cards numbered 1-12. He picks one card and then replaces it. Then he picks another card. What is the probability he picks a 1 and then a 12?
Final answer:
The probability of picking a 1 and then a 12 from a deck of cards numbered 1-12 with replacement is 1/144, since each event is independent and each card has an equal chance of being selected.
Explanation:
The student asked about the probability of selecting a 1 and then a 12 from a deck of cards numbered 1-12, with replacement in between the picks. To find this, we need to consider the events independently, since the card is replaced after the first draw, meaning the probability of the second draw is unaffected by the first.
The formula to calculate the probability of independent events is P(A and B) = P(A) × P(B), where P(A) is the probability of the first event and P(B) is the probability of the second event occurring. Since each card has an equal chance of being picked from the deck, and there are 12 cards in total, the probability of picking any specific card, like a 1 or a 12, is 1/12.
Therefore, the probability of picking a 1 first and then a 12 is P(1 and then 12) = P(1) × P(12), which is equal to (1/12) × (1/12) = 1/144. So, the final probability is 1/144, or about 0.00694.
Which are rational numbers?
Check all that are true.
3⁄456
3⁄1
3⁄0
-191⁄32
PLEASE HELP! A class has an average score of 75%. A test is taken with an average score of 60%. The test is graded on a curve so that 60%=75%. If Emalie's original score is 72%, what is her new grade after the curve? This is real life, as I'm trying to figure out my exam grade believe it or not!
Answer:
1.032%
Step-by-step explanation:
an item is regularly priced at $75 it is now priced at a discount of 55% off the regular price
Answer:
$41.25
Step-by-step explanation:
part=%(whole)
x=55%(75)
x=0.55(75)
x=41.25
The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both increased by 2, the fraction is now equal to .
If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?
Question:
The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both decreased by 2, the fraction is now equal to [tex]\frac{1}{2}[/tex].
If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?
5n = 3d and n - 2 = 2d - 4
5n = 3d and 2n - 4 = d - 2
3n = 5d and 2n - 4 = d - 2
Answer:
5n = 3d and 2n – 4 = d – 2
Solution:
Let n be the numerator of the fraction and d be the denominator of the fraction.
Given the numerator and denominator of a fraction are in the ratio of 3 to 5.
This can be written as n : d = 3 : 5.
⇒ [tex]\frac{n}{d}= \frac{3}{5}[/tex] – – – – (1)
Do cross multiplication, we get
⇒ 5n = 3d
When the numerator and denominator are decreased by 2, the fraction is equal to [tex]\frac{1}{2}[/tex].
⇒ [tex]\frac{n-2}{d-2}= \frac{1}{2}[/tex]
Do cross multiplication, we get
⇒ 2(n –2)=1(d – 2)
⇒ 2n – 4 = d – 2
Hence, 5n = 3d and 2n – 4 = d – 2 can be used to solve the problem.
Answer:
5n = 3d and 2n – 4 = d – 2 is the answer
Step-by-step explanation:
At the fabric shop I buy 378 metres of orange fabric, 107
metres of yellow fabric and 467 metres of purple fabric. I
have used 16 metres of the orange fabric, 27 metres of yellow
fabric and 12 metres of purple fabric.
How many metres of fabric do I have left in total?
For questions 5-8, evaluate the expression for x = 6 and y =17
5. 4x + 5y
6. 2x + (20 - y )
7. x ÷ 3 + y
8. 4y ÷ 2 + ( 8x + 10)
The expressions for the given questions are substituted and solved using the provided values of x and y. The solutions for the four questions respectively are 109, 15, 19, and 92.
Explanation:To evaluate the expressions for questions 5-8, you will need to substitute the values of x and y into each given expression.
For 4x + 5y, the solution would be 4*6 + 5*17 = 24 + 85 = 109 For 2x + (20 - y), the solution would be 2*6 + (20 - 17) = 12 + 3 = 15 For x ÷ 3 + y, the solution would be 6 ÷ 3 + 17 = 2 + 17 = 19 And for 4y ÷ 2 + (8x + 10), the solution would be 4*17 ÷ 2 + ( 8*6 + 10) = 34 + 58 = 92
Through these steps, you can understand how to substitute and solve such expressions.
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What is 17.0891 rounded to the nearest tenth?
Answer:
17.1
Step-by-step explanation:
The required round of number 17.0891 to the nearest tenth is 17.1.
Given that,
To round the number 17.0891 to the nearest tenth.
The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Given number,
17.0891
Since the number on the tenth place after the decimal is 0 and the value next is 0.08 which is near to 0.1 so the number on the tenth place will increase by a unit and the whole number become,
= 17.1
Thus, the required round of number 17.0891 to the nearest tenth is 17.1.
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After submitting what is the first operation performed when evaluating 5+ (9x-3) divided 2 for x=5?
Answer:
The first operation performed when evaluating the given expression [tex]5+(\frac{9x-3}{2})[/tex] for x=5 is given below :
Step 1: Put x=5 in the above given expression we get
[tex]5+(\frac{9(5)-3}{2})[/tex]
Step-by-step explanation:
Given equation is [tex]5+(\frac{9x-3}{2})[/tex] for x=5
To find the first operation performed when evaluating the given expression [tex]5+(\frac{9x-3}{2})[/tex] for x=5
[tex]5+(\frac{9x-3}{2})[/tex]
Step 1: Put x=5 in the above expression we get
[tex]5+(\frac{9(5)-3}{2})[/tex]
[tex]=5+(\frac{45-3}{2})[/tex]
[tex]=5+(\frac{42}{2})[/tex]
[tex]=5+21[/tex]
[tex]=26[/tex]
Therefore [tex]5+(\frac{9x-3}{2})[/tex] for x=5 is 26
Therefore [tex]5+(\frac{9x-3}{2})=26[/tex] for x=5
What is the y intercept of a graph containing the two points (3,1) and (7,-2)?
The y intercept of a graph containing the two points (3,1) and (7,-2) is [tex]\frac{13}{4}[/tex]
Solution:
Given points are (3, 1) and (7, -2)
The equation of line in slope intercept form is given as:
y = mx + c ------- eqn 1
Where, "m" is the slope of line and "c" is the y intercept
Let us first find the slope of line
The slope of line is given as:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here the points are (3, 1) and (7, -2)
[tex](x_1, y_1) = (3, 1)\\\\(x_2, y_2) = (7, -2)[/tex]
Substituting in formula, we get
[tex]m = \frac{-2-1}{7-3}\\\\m = \frac{-3}{4}[/tex]
To find the y intercept:
[tex]\text{Substitute } m = \frac{-3}{4} \text{ and } (x, y) = (3, 1) \text{ in eqn 1 }[/tex]
[tex]1 = \frac{-3}{4} \times 3 + c\\\\1 = \frac{-9}{4} + c\\\\ \text{Simplify the above equation } \\\\1 = \frac{-9+4c}{4}\\\\4 = -9 + 4c\\\\13 = 4c\\\\\text{Divide both sides by 4 }\\\\c = \frac{13}{4}[/tex]
Thus y -intercept is [tex]\frac{13}{4}[/tex]
Ali runs 7 miles in 60 minutes. At the same rate, how many miles would he run in 24 minutes
Answer:
Ali would run 2.8 miles in 24 minutes.
I NEED HELP WITH THIS PROBLEM ASAP PLEASE!! THANK YOU VERY MUCH!! <3
Answer:
OPTION C
OPTION E
Step-by-step explanation:
Distributive property of Addition:
a(b + c) = ab + bc
In other words, 'a' is distributed over 'b' and 'c'.
Also, note that a mixed fraction, of the form [tex]$ \textbf{c} \frac{\textbf{x}}{\textbf{y}} = \textbf{c} + \frac{\textbf{x}}{\textbf{y}} $[/tex]
If a mixed fraction is of the type [tex]$ \textbf{-p}\frac{\textbf{q}}{\textbf{r}} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{-(p + } \frac{\textbf{q}}{\textbf{r}}) \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{-p} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{q}}{\textbf{r}} $[/tex]
OPTION A:
[tex]\textbf{3} \bigg ( \textbf{-4} \frac{\textbf{1}}{\textbf{2}} \bigg )[/tex]
This can be written as: [tex]$ 3 \bigg ( - 4 - \frac{1}{2} \bigg ) $[/tex]
Now, we distribute 3 over -4 and [tex]$ -\frac{1}{2} $[/tex].
[tex]$ = 3(-4) + 3\bigg (-\frac{1}{2} \bigg ) $[/tex]
Therefore, OPTION A is incorrect.
OPTION B: [tex]$ \textbf{2} \frac{\textbf{1}}{\textbf{4}} \bigg ( \textbf{1} \frac{\textbf{3}}{\textbf{4}} \bigg ) $[/tex]
Now, this is written as: [tex]$ 2 + \frac{1}{2} \bigg ( 1 + \frac{3}{4} \bigg ) $[/tex]
We have distribute 2 and [tex]$ \frac{1}{2} $[/tex] separately over 1 and [tex]$ \frac{3}{4} $[/tex].
So, we should have [tex]$ 2 (1) + 2 \bigg ( \frac{3}{4} \bigg ) + \frac{1}{2} (1) + \frac{1}{2}. \frac{3}{4} $[/tex]
So, OPTION B is incorrect.
OPTION C: [tex]$ \textbf{-4} \bigg( - 5 \frac{\textbf{1}}{\textbf{3}} \bigg ) $[/tex]
[tex]$ = - 4 \bigg ( -5 - \frac{1}{3} \bigg) $[/tex]
[tex]$ = -4(-5) + (-4) \bigg (- \frac{1}{3} \bigg ) $[/tex]
Hence, OPTION C is correct.
Similar method will help us know that OPTION D has used the Distributive property incorrectly and OPTION E has.
So, the answers are:
OPTION A
OPTION C
OPTION E
Carol types 57 words in 3 minutes.how many words would she type in 1 hour?
Answer:
1,140 words
Step-by-step explanation:
57/3 = 19 words per minute
there are 60 minutes in an hour
19x60 = 1140
If Carol is able to type 57 words in 3 minutes, then in one hours time she will be able to type 1140 words.
Number of words Carol typed in 1 hours is;Let the number of words typed in 1 hours be represented as y
So that;
57 words are typed in 3 min
We know that 60 minutes makes 1 hour
57 words typed in 0.05 hour
y words typed in 1 hours
We cross multiply
57 words × 1 hour = y × 0.05 hour
y = 57hours / 0.05 hours
y = 1140 words
If Carol is able to type 57 words in 3 minutes, then in one hours time she will be able to type 1140 words.
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The circumference of great circle of a hemisphere is 44 cm. find the total surface area of the hemisphere
Answer:
I didn't know if you meant that the circumference of tje hemisphere was 44 or if the circumference of the cirkel in which the hemisphere exists is 44 but you rearrange the numbers.
Step-by-step explanation:
The formula for calculating a circumference is 2×pi×r, with r as tje radius of the cirkel. So in this instance we get 2×pi×r=44. r=44/(2×pi)=7.00 centimeters. The total surface area of a cirkel=pi×r^2=pi×7.00^2=154.06 meters squared. 154.06/2=77.03 meters squared (hemisphere is half of a cirkel)
To find the total surface area of the hemisphere, first find the radius of the hemisphere using the formula for circumference. Then, use the formula for the total surface area of a hemisphere to calculate it.
Explanation:To find the total surface area of the hemisphere, we need to first find the radius of the hemisphere. Since the circumference of the great circle is given as 44 cm, we can use the formula for circumference to find the radius: C = 2πr. Thus, 44 = 2πr. Solving for r, we have r = 44/(2π) = 7 cm.
The total surface area of a hemisphere is given by the formula A = 3πr^2. Plugging in the value of the radius, we get A = 3π(7^2) = 3π(49) = 147π cm^2.
So, the total surface area of the hemisphere is 147π cm^2.
Help me please! 20 points!
Answer:
Step-by-step explanation:
a) increase
Increase = 200 -130 = 70
Percent increase = (70/130)*100 = 70*100/130 = 7*100/13
= 700/13
= 53.85%
Answer:
a) increase
Step-by-step explanation:
how to distribute -2(x-3)^2
The distributed form of -2(x-3)^2 is -2x^2 + 12x - 18.
Step-by-step explanation:
The given question is -2(x-3)^2
step 1 :The formula for (a-b)^2 = a^2 - 2ab + b^2
step 2 :Here, the term (x-3)^2 = x^2 - (2*3x) + 3^2
= x^2 - 6x + 9
step 3 :The expanded form = -2 (x^2 - 6x + 9)
step 4 : where -2 can be distributed to each term inside the bracket.
Therefore, -2(x^2 - 6x + 9) = -2x^2 + 12x - 18
If a triangle is a right triangle, then the triangle has 90 angle.
Answer:
True
Step-by-step explanation:
Yes, but not all angles in the triangle will be 90 degrees.
I need to solve these systems using substitution.
y= -4x + 2
y= x - 3
Could you please show your steps so I can learn too?
y is some number and it is equal to -4x+2
y being that same number is also equal to x-3
therefore, we can equate -4x+2 and x-3 to get x-3 = -4x+2
This is the same as starting with y = -4x+2 and replacing the y with x-3
----------------
Let's solve for x
x-3 = -4x+2
x-3+4x = -4x+2+4x .... add 4x to both sides
5x-3 = 2
5x-3+3 = 2+3 .... add 3 to both sides
5x = 5
5x/5 = 5/5 .... divide both sides by 5
x = 1
With this x value, you can now find the y value. Pick any equation that has x and y in it. If we picked the first equation, then
y = -4x+2
y = -4*1+2 ... plug in x = 1
y = -4+2
y = -2
Or we can pick the second equation
y = x-3
y = 1-3 .... plug in x = 1
y = -2
-------------------------------------------------------------------------
The solution to the system is (x,y) = (1, -2)Graphing the two lines will have them intersect at this location.
Please help!!!!! ASAP
Answer:
ok
Step-by-step explanation:
asap
I need help please and thank you
Answer:
The other 2 angles combined measure 70
Step-by-step explanation:
all of a triangle's angles together measure 180.
If one angle is 110 the other 2 would be 70.
I have to do this ixl please help me with the missing blanks please
Which of the following statements best explains how the graphs misrepresent the data?
A.The graphs were created with different colors.
B.The graph for City B makes its population appear much smaller, but its population is only a little smaller than City A.
C.The graphs use different scales, making it appear that City A has a larger population than City B.
D.The graphs do not include information for the years between 1950 and 2000, so there is not enough information to compare their populations.
Answer:
i believe the answer is C
What is 13.2857142857 as a fraction
the fraction form of 13.2857142857 is[tex]\( \frac{1195714285713}{90000000000} \).[/tex]
To convert the decimal 13.2857142857 into a fraction, we can follow these steps:
Step 1: Let x = 13.2857142857
Step 2: Multiply x by 10 to move the decimal one place to the right:
x = 13.2857142857
10x = 132.857142857
Step 3: Subtract the original x from 10x to eliminate the decimal:
10x - x = 132.857142857 - 13.2857142857
9x = 119.5714285713
Step 4: Simplify the equation:
9x = 119.5714285713
Step 5: Divide both sides by 9:
[tex]\[x = \frac{119.5714285713}{9}\][/tex]
Step 6: Simplify the fraction:
[tex]\[x = \frac{1195714285713}{90000000000}\][/tex]
Now, the fraction form of 13.2857142857 is[tex]\( \frac{1195714285713}{90000000000} \).[/tex]
If angle 1 is 110°, what would the other angle measures
have to be in order for m ll n and
all p?
Angle 2=
Angle 3 =
Angle 4 =
Answer:
Angle 2= 110 degrees
Angle 3 = 70 degrees
Angle 4 = 70 degrees
Step-by-step explanation:
Finding angle 2
In the figure attached below,the angles 1 and 2 Corresponding angles
When two lines are crossed by another line that is called the Transversal, then, the angles in matching corners are called corresponding angles.
Corresponding angles are equal so
angle 2 = 110 degrees
Finding angle 3
Similarly 2 and 3 are consecutive angles and Consecutive angles are supplementary . That is the sum of the consecutive angles is 180 degree
then
angle 2 +angle 3 = 180
110 + angle 3 = 180
angle 3 = 180 -110
angle 3 = 70 degrees
Finding angle 4
Now angle 3 and angle 4 are alternate interior angle and they are equal
angle 3 = angle 4
so angle 4 is 70 degree
Answer:
110
70
70
Step-by-step explanation:
cause i got it right