Write the equation of a horizontal line that passes through the point (3, -3).
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Trinh drew a triangle that had coordinates (1, –2), (4, –2), and (1, –4). She translated the figure 4 units left and 5 units up. What are the coordinates of the new figure?
(–4, 2), (–1, 2), and (–4, 0)
(–3, –2), (0, –2), and (–3, –4)
(–3, 3), (0, 3), and (–3, 1)
(1, 3), (4, 3), and (1, 1)
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Which summation formula represents the series below? 12 – 24 + 48 – 96
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12 – 24 + 48 – 96
will be calculated as follows:
first term,a=12
common ratio=+/-2
thus the sum will be:
(i=1)Σ[12(-2)^(i-1)]
Thus the answer:
(i=1)Σ[12(-2)^(i-1)]
Answer: B
Step-by-step explanation:
according to the U.S. census bureau, the population of Hawaii in 2010 was 1,360,301 and it was growing at an annual rate of 1.2%. Predict the population in Hawaii in 2032
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If 30 fair dice are rolled find the approximate probability that the average number ofo dots is between 2 and 4
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The probability that the average number of dots is between 2 and 4 when rolling 30 fair dice is 0.9441.
what is probability?Probability is the branch of mathematics that deals with the study of random events or phenomena. It involves the quantification of uncertainty and the measurement of the likelihood of occurrence of an event.
The average number of dots on a fair die is
= (1+2+3+4+5+6)/6
= 3.5.
We can model the sum of the numbers on the 30 dice as a normal distribution with mean
= (30)(3.5) = 105
and, standard deviation √(30)(35/12) ≈ 9.13.
Let X be the sum of the numbers on the 30 dice, and let Y be the average number of dots. Then Y = X/30.
We want to find P(2 ≤ Y ≤ 4). This is equivalent to P(60 ≤ X ≤ 120), since Y = X/30.
Using the normal distribution, we can standardize X to get:
Z = (X - 105) / 9.13
Then we can compute the probability as:
P(60 ≤ X ≤ 120)
= P[(60 - 105) / 9.13 ≤ Z ≤ (120 - 105) / 9.13]
≈ P(-4.93 ≤ Z ≤ 1.64)
Using a standard normal distribution table or calculator, we can find that P(-4.93 ≤ Z ≤ 1.64) ≈ 0.9441.
Therefore, the approximate probability that the average number of dots is between 2 and 4 when rolling 30 fair dice is 0.9441.
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The sum in a half adder can be represented by what boolean expression (assuming a
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If they are both 0, the sum is 0. If they are both 1, the sum is 0 and the carry is 1.
This is the XOR logic gate; either one of the two inputs, but not both. In boolean algebra, XOR can be represented as: ¬AB + A¬B
complete the general solution to y=cos^-1(1) for K a whole number
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Answer:
If the equation is exactly the one you posted then the unique answer is:
[tex]y = 0[/tex]
or what is the same:
[tex]y=0K[/tex]
Explanation:
If your equation is exactly the one you posted then it has only one solution: y = 0
Because the range of [tex]y=\cos^{-1}(x)[/tex] is the interval [tex][0, \pi][/tex]
The meaning of [tex]\cos^{-1}(1)[/tex] is to find the angle whose cosine is 1.
In the range of the function arccosine the only angle whose cosine is 1 is the angle 0.
But if your equation was the following one:
[tex]\cos(y)=1[/tex]
Then in that case we would have infinite solutions since it will be the set:
[tex]y=\cos^{-1}(1)+2K\pi[/tex] where K is an integer, since the period of cosine is [tex]2\pi[/tex]
So, in such a case the solution set would be:
[tex]y=0+2K\pi=2K\pi[/tex]
But for the equation you posted, the unique solution is: y = 0 or what is the same y = 0K
Two angles whose measures add up to 90º are called?
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Drag and drop the symbols to enter the equation of the circle in standard form with center and radius given. Center (5, -3), radius = 1
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The standard form of the equation of a circle is:
[tex](x - a) {}^{2} + (y - b) {}^{2} = r {}^{2} [/tex]
With (a, b) representing the centre and r representing the radius of the circle.
Since the centre of the circle is (5, -3) and the radius is 1, we get the following equation:
[tex](x - 5) {}^{2} + {(y + 3)}^{2} = 1[/tex]
A class is trying to eliminate t from the parametric equations x=t^2+3 and y=4t. Beth says that she can write t=sqrt(x-3) to eliminate the parameter. Why is this wrong?
She should have added 3 to x, not subtracted.
She should always solve for t as a function of y.
She should have taken both the positive and negative square root.
She should first substitute y for t before solving.
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Because when a number is squared, even if it is negative it can become positive,
so taking square should include + and - to the answer.
Beth says that she can write that she should have taken both the positive and negative square root to eliminate the parameter. Therefore, option (c) is correct.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
We have to find the error which is done by Beth to eliminate the parameter. So, we will take the first equation and do all the steps to find the error and get the desired result.
Given that, x=t²+3 and y=4t
Try find the expression of "t" in terms of "x". We will use equation (1) and we have
x-3=t²
t=√(x-3)
Thus, Beth says that she can write that she should have taken both the positive and negative square root to eliminate the parameter. Therefore, option (c) is correct.
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How to find the length of a rectangle when given the height?
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The formula for area is:
Area = length • width
If you were given the width and area of the rectangle you would be able to find the length by doing inverse operations. In this case, the opposite of multipication is division
Example: 56 = l • 8
56 / 8 = 7
56 = 7 • 8
The length is 7.
I hope this helps!
The length of a rectangle can be found by dividing the area of the rectangle by its height if the area is known. Without the area, additional information is necessary to calculate the length.
To find the length of a rectangle when given the height, we typically need additional information such as the area or the aspect ratio of the rectangle. However, without that information, directly calculating the length is not possible. Let's explore a scenario where we have the area of the rectangle. In such a case, if we are given the area (A) of the rectangle and the height (h), we can use the formula for the area of a rectangle which is A = length times height. Solving for the length (l), we rearrange the formula to get l = A/h. For instance, if the area of the rectangle is 150 square centimetres and the height is 10 centimetres, the length would be 150 cm2 / 10 cm = 15 cm. It's also important to consider proportions when scaling shapes.
Ernie is making a cylinder-shaped container to store his pens. The container has a base on one end and an opening on the other end. He is going to spray paint the outside of the container. The container has a diameter of 3 inches and a height of 18 inches.
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We have then:
A = pi * r ^ 2 + 2 * pi * r * h
Where,
r: cylinder radius
h: cylinder height
Substituting values:
A = 3.14 * (3/2) ^ 2 + 2 * 3.14 * (3/2) * 18
A = 176.625 in ^ 2
Answer:
The amount of paint needed is:
A = 176.625 in ^ 2
Barbara is making bracelets to sell on her Etsy site. It costs her $0.79 per bead and she needs 22 beads per bracelet. She sells her bracelets for $28 each. What is the percent markup per bracelet?
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What are the zeros of f(x) = x2 – 10x + 25?
A. x = –5 and x = 10
B. x = –5 only
C. x = –5 and x = 5
D. x = 5 only
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(x-5) * (x-5)
The answer is 5
The zeros of a function are also known as the roots of the function
The correct option for the zeros of f(x) = x² - 10·x + 25 is the option D.
D. x = 5 only
The reasons why the selected option is correct are given as follows:
The given equation is presented as follows;
f(x) = x² - 10·x + 25
Solution:
The zeros are the values of x when the equation is equal to zero which is given as follows;
x² - 10·x + 25 = 0
By observation, we have;
Given that the coefficient of x² is one, and we have that 25 = (-5) × (-5), and -10 = -5 + (-5), therefore, we can write;
0 = x² - 10·x + 25 = (x - 5)·(x - 5)Which gives, either x = 5 , or x = 5Therefore, the zeros of the function is 5 only, and the correct option is option D.
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saidhari bought a toaster oven for $60. this price was 1/4 off the list price. What was the list price
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Final answer:
The list price of the toaster oven was $80.
Explanation:
To find the list price, we need to determine the price of the toaster oven before the discount. Let's call the list price 'x'. The discount is 1/4 off the list price, so the discounted price is 3/4 of the list price. We can set up the equation 3/4 * x = $60 to find the value of 'x'. To solve for x, we can multiply both sides of the equation by 4/3: (3/4 * 4/3) * x = $60 * 4/3. Simplifying the equation gives us x = $80.
in a cylinder the radius and height was quadrupled. How much bigger would the new surface area be then the original surface area.
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A = 2 * pi * r ^ 2 + 2 * pi * r * h
Where,
r: radio
h: height
The area when the dimensions are modified is:
A '= 2 * pi * (4r) ^ 2 + 2 * pi * (4r) * (4h)
Rewriting we have:
A '= 16 * 2 * pi * r ^ 2 + 16 * 2 * pi * r * h
A '= 16 (2 * pi * r ^ 2 + 2 * pi * r * h)
A '= 16A
Answer:
the new surface area would be 16 times bigger than the original surface area
if in a cylinder the radius and height was quadrupled
so
the scale factor is equal to 4
scale factor=4
and
new surface area=[scale factor]²*original surface area
new surface area=[4]²*original surface area
new surface area=16*surface area original
therefore
the new surface area will be 16 times the original surface area.
alternative method
we know that
surface area of cylinder=2*[area of the base]+perimeter of the base*height
area of the base=pi*r²
perimeter of the base=2*pi*r
original surface area=2*[pi*r²]+[2*pi*r]*h-----> 2*pi*r*[r+h]
if the radius and height was quadrupled
so
new surface area=2*pi*(4*r)*[4r+4h]-----> 2*pi*(4*r)*4*[r+h]
new surface area=16*[2*pi*r*(r+h)]----> 16*[original surface area]
the answer is
the new surface area will be 16 times the original surface area.
If Kareem’s living room has an area of 225 square feet, how much will he spend to carpet his living room?
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Answer: $ 568.99
Because 18.99+22 x 225/9 = 568.99
Answer: 568.99
Step-by-step explanation: your mom
this will be worth ten points
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To prove this one way, you can show the multiplication of the quotient and divisor. If the division was correct, it would end up as the value of the dividend:
84 * 15 = 1260
1260 = 1260
To prove this another way, you can show 84 being added 15 times and seeing if it totals 1260:
84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 = 1260
1260 = 1260
Answer:
1260/15=84
Step-by-step explanation:
1200/15=80 and 60/15=4
80 + 4 = 84.
Another way is 15 + 15 + 15 and keep counting 84 times and you would get 84
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What is the first step to simplify the expression: [–23 – [5 · (2 – 4)]] ÷ 32
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Short answer: 2 - 4
Why?
When you have an equation with parenthesis, you do those first. When you have parenthesis inside of parenthesis, you do that first.
Hope this helped you! ♥
Answer:
According to PEDMAS , We first simplify the PARENTHESES
[5 · (2 – 4)] = [5· -2] = -10
Step-by-step explanation:
Given expression [–23 – [5 · (2 – 4)]] ÷ 32
We have to find the first step to simplify the given expression.
We apply PEDMAS
P stands for PARENTHESES
E stands for EXPONENTS
D stands for DIVIDE
M stands for MULTIPLY
A stands for ADDITION
S stands for SUBTRACTION.
So, according to PEDMAS , We first simplify the PARENTHESES
Thus, [5 · (2 – 4)] = [5· -2] = -10
Graph f(x)=- square root -x
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[tex]x=0\to f(0)=-\sqrt0=0\to(0;\ 0)\\\\x=-0.25\to f(-0.25)=-\sqrt{-(-0.25)}=-\sqrt{0.25}=-0.5\to(-0.25;-0.5)\\\\x=-1\to f(-1)=-\sqrt{-(-1)}=-\sqrt1=-1\to(-1;-1)\\\\x=-4\to f(-4)=-\sqrt{-(-4)}=-\sqrt4=-2\to(-4;-2)[/tex]
The graph of function f (x) = - √- x is shown in image.
We have to given that,
Graph the function,
f (x) = - √- x
Here, Function is defined as,
f (x) = - √- x
At x = 0;
f (x) = - √-0
f (x) = 0
Plot the graph of function f (x) = - √- x.
Hence, The graph of function f (x) = - √- x is shown in image.
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Need help with these 2 problems I’m pretty sure I got the first one right but I don’t know how to do the second one please and thank you!!
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where
[tex]A[/tex] is the final amount after [tex]t[/tex] years
[tex]P[/tex] is the initial investment
[tex]r[/tex] is the interest rate in decimal form
[tex]t[/tex] is the number of years
Mathematical steps for solving the problem:
We can infer from our problem that you are going to invest $800-$640=$160 in your savings account, so [tex]P=160[/tex]. To convert the interest rate to decimal form, we are going to divide the rate by 100%
[tex]r= \frac{4.5}{100} =0.045[/tex]. Since you are leaving the money in your savings account for a year, [tex]t=1[/tex]. Lets replace those values in our formula:
[tex]A=P(1+rt)[/tex]
[tex]A=160[1+(0.045)(1)][/tex]
[tex]A=160(1+0.045)[/tex]
[tex]A=160(1.045)[/tex]
[tex]A=167.2[/tex]
We can conclude that your total savings after buying the refurbished laptop are: $167.2
A Student said the volume of a cylinder with a 3-inch diameter is two times the volume of a cylinder with the same height and a 1.5-inch radius. What is the error?
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A lawn roller is 1 m wide and 80 cm high. What area is covered in each revolution
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A = 2 * pi * r * l
Where,
r: roller radius
l: roller width
We have then:
A = 2 * 3.14 * (0.80 / 2) * 1
A = 2.512 m ^ 2
Answer:
The area that is covered in each revolution is:
A = 2.512 m ^ 2
what is the measure of the angle?
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Measure of the angle=55°+180°=235°
We can conclude that the measure of the angle in the picture is 235°
Simplify the expression.
(–1 + 6i) + (–4 + 2i)
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= -1 + 6i - 4 + 2i
= -5 + 8i
Hope it helped!
Which value is the 10th term in the sequence:-62,-47,-32,-17,-2?
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Sure!!!
Training course a takes 9 weeks and 4 days to complete.training course b takes 54 days to complete.how much longer does training course a take than training coure b to complete
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[tex]7 \times 9 + 4 = 67 \\ 67 - 54 = 13[/tex]
Training course A takes 13 more days than training course B.
Training course A takes 13 days longer than training course B to complete.
Explanation:To find how much longer training course A takes than training course B to complete, we need to compare the durations of the two given courses with given values.
Training course A takes 9 weeks and 4 days to complete, which is found to be :
9 x 7 + 4 = 67 days in total.
Training course B takes 54 days to complete.
To find the difference, we subtract the duration of course B from the duration of course A:
67 - 54 = 13 days.
Therefore, training course A takes 13 days longer than training course B to complete.
A bag contains 2 blue, 4 green, and 3 white chips. What is the probability of drawing a white chip then another white chip without replacement?
A.) 7/9
B.) 8/81
C.) 2/3
D.) 1/12
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total white chips = 3
probability of picking white first = 3/9 = 1/3
after taking one chip there would be 9-1 = 8 chips left
and 3-1 2 white chips left
probability of picking 2nd white chip = 2/8 = 1/4
probability of picking both = 1/3 x 1/4 = 1/12
answer is D
The perimeter of a rectangular garden is 43.8 feet. Its length is 12.4 feet. What is the width
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43.8 =2(12.4 + w)
21.9=12.4 +w
21.9-12.4 = w
w=9.5 feet
First you know what the length is. You must find the measurement of both combined.
12.4 x 2 = 24.8 (Length)
Subtract this number from the perimeter. 43.8 - 24.8 = 19.
19 is your width multiplied by two. The total measurement of both, to find just the width divide by 2.
19 / 2 = 9.5 (WIDTH)
simplify
3 (2x+4y-2z)+7 (x+y-4z)
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What is the standard deviation of the following data set rounded to the nearest tenth?
51.8, 53.6, 54.7, 51.9, 49.3
A.3.4
B.3.3
C.1.9
D.1.8
Answers
the standard deviation of the data set will be found as follows:
Var=∑(x-μ)²/(n)
μ-mean
μ=(51.8+53.6+54.7+51.9+49.3)/5
μ=261.3/5=52.26
Next:
∑(x-μ)²=(51.8-52.26)²+(53.6-52.26)²+(54.7-52.26)²+(51.9-52.26)²+(49.3-52.26)²
∑(x-μ)²=16.852
thu
Var(x)=16.852/(5)=3.3704
Hence the standard deviation will be:
σ=√3.3704=1.835865~1.8
Answer: D] 1.8
Answer:
1.8
Step-by-step explanation: