Answer:
Step-by-step explanation:
If the tank holds 2500 liters and there are already 750 liters in there, he only needs to buy 1750 liters.
If he is saving 6%, he is still spending 94%, so
.94(58.4) = 54.896 (what he'll be paying per liter after the 6% comes off, then
54.896(1750) = $96,068
In 2014, the population of Ohio was 11.59 million people. One-hundred years earlier the population was 5.109 million people. Using scientific notation, how much did the population grow over the hundred-year span?
The answer is the population grew over the hundred-year span by [tex]6.481*(10)^6[/tex]
Given that in 2014, the population of people in Ohio = [tex]11.59[/tex] million
Also given that One-hundred years earlier of the year 1914, the population = [tex]5.109[/tex] million people
One-hundred years earlier in the year 2014 = 2014 [tex]- 100[/tex] years
One-hundred years earlier in the year 2014 = Year 1914
The scientific notation of the year 2014 population is [tex]11.59*(10)^6[/tex]
The scientific notation of the year 1914 population is [tex]5.109*(10)^6[/tex]
How much did the population grow over the hundred-year span?
Growth of the population from 1914-2014 = [tex]11.59*(10)^6 - 5.109*(10)^6[/tex]
Growth of the population from 1914-2014 = [tex]6.481*(10)^6[/tex]
Conclusion: The population grew over the hundred-year span by [tex]6.481*(10)^6[/tex]
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Select the correct answer.
Select the function that defines the given sequence.
-8, -20, -50, –125, 625,...
ОА
- 1)
f(n) = -8-()
n-
OB.
- 1)
= -8.(29)
OC f(1) = -8
f(n) = f(n − 1), for n = 2, 3, 4, ...
OD. (1) = 8
f(n) = - . 1(n − 1), for n = 2, 3, 4, ...
Answer:
Option C
Step-by-step explanation:
f(1) = -8
f(2) = -5/2×-8 = -20
f(3) = -5/2×-20 = -125
.
.
.
So option C is the answer
Answer:
C. a1 = -8
an = an-1 * 5/2 for n >1
Step-by-step explanation:
-8, -20, -50, –125, 625,...
We need to find the common ratio
Take the second term and divide by the first term
-20/-8 = 5/2
Take the third term and divide by the second term
-50/-20 = 5/2
The common ratio is 5/2
A geometric sequence is
an = a1 * r^(n-1)
an = -8 *(5/2)^(n-1)
We can also write a recursive formula
a1 = -8
an = an-1 * 5/2 for n >1
What is the slope of the line passing through the points (6,1) and (-3,-4)?
Answer:
5/9
Step-by-step explanation:
y2-y1/x2-x1 = 5/9
Question 6 plz show ALL STEPS
Step-by-step explanation:
6a. Both the x and y coordinates are negative so this means isn't must be in the Third Quadrant.
6b. The measure of this using the unt circle is
[tex] \cos(x) - \frac{1}{2} [/tex]
[tex] \sin(x) = - \frac{ \sqrt{3} }{2} [/tex]
In the unit circle, this occurs about
an angle of 240 degrees. We can find coterminal angles within the interval of 2 pi to -2 pi. Just subtract 260 from theta.( which is 240)
[tex]240 - 360 = - 120[/tex]
So the angles in the interval is
240, -120.
6c. pi/2 is the same as 90 degrees so this means that
[tex](240 + 90) = 330[/tex]
In the unit circle, we know that at 330 degrees,
[tex] \cos(330) = \frac{ \sqrt{3} }{2} [/tex]
[tex] \sin(330) = \frac{1}{2} [/tex]
So the coordinates are
(sqr root of 3/2, 1/2).
6d. pi is the same as 180 degrees so this means that
[tex](240 - 180) = 60[/tex]
In the unit circle, we know that 60 degrees,
[tex] \cos(60) = \frac{1}{2} [/tex]
[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]
So the coordinates are
(1/2, sqr root of 3/2)
Which sequence is arithmetic?
O 2, 6, 18, 54, ...
O 3, 6, 12, 24, ...
O 11, 14, 17, 20, ...
O 7, 11, 13, 18, ...
Answer:
11, 14, 17, 20, ...
Step-by-step explanation:
An arithmetic sequence is one where each term increases by the same number every time. This is called the common difference and is always added to the previous term to get the current term. The only sequence that follows this is the third once. Every term increases by 3; therefore, it is an arithmetic sequence.
A function does not have any x-intercepts. What
might be true about its domain and range?
The domain exists on all real numbers i.e {x∈R}∈
The range exists all on real numbers except at y = 0
Domains are all input values of a function for which the function exists while ranges are all the output values for which the function exists.
Since the x-intercept of a function exists at where y = 0, this means that the point where a function does not have any x-intercepts are all other points on the graph except at y = 0.
The following statements are therefore true;
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Write an algebraic expression for each person’s share, if P people share 16 slices of pizza equally.
Answer:
P /16
Step-by-step explanation:
Take the total amount, P and divide by the number of people sharing, 16
P /16
Find the greatest common factor of these two expressions.
14w5y8x2 and 7w6x2
Answer:
[tex]7w^{5}x^{2}[/tex]
Step-by-step explanation:
We can start by looking at each variable and and constant separately. In the first one, the constant part is 14 and in the second its 7. We can notice that the GCF of these two is 7. Next we have the part with w. The first one is w^5 while the second is w^6. We can notice that we can factor w^5 out of both, so it is the GCF. We can notice that only the first one has a y, so we can ignore it since it is not in common with both expressions. Lastly, we have x: the first has x^2 and the second has x^2 as well. They are the same, so the GCF would just be x^2.
Now, we can multiply the results together to get the GCF of the whole expressions:
7 * w^5 * x^2 = [tex]7w^{5}x^{2}[/tex]
A certain drug is used to treat asthma. In a clinical trial of theâ drug, 17 of 258 treated subjects experienced headachesâ (based on data from theâ manufacturer). The accompanying calculator display shows results from a test of the claim that less than 11â% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete partsâ (a) throughâ (e) below. â
1-PropZTest
prop<0.11
z=â2.264337000
p=0.0117766978
p=0.0658914729
n=258
a. Is the testâ two-tailed, left-tailed, orâ right-tailed?
b. What is the best statistics?
c. What is the P-value?
d. What is the nut hypothesis and what do you conclude who det hypothesis?
Identify the null hypothesis.
A. H0: pâ 0.11.
B. H0: p=0.11.
C. H0: p<0.11.
D. H0: p>0.11.
Decide whether to reject the null hypothesis.
A. Reject the null hypothesis because theâ P-value is greater than α.
B. Fail to reject the null hypothesis because theâ P-value is less than or equal to α.
C. Reject the null hypothesis because theâ P-value is less than or equal to α.
D. Fail to reject the null hypothesis because theâ P-value is greater than α
e. What is the finalâ conclusion?
A. There is not sufficient evidence to warrant rejection of the claim that less than 11â% of treated subjects experienced headaches.
B. There is not sufficient evidence to support the claim that less than 11â% of treated subjects experienced headaches.
C. There is sufficient evidence to support the claim that less than 11â% of treated subjects experienced headaches.
D. There is sufficient evidence to warrant rejection of the claim that less than 11â% of treated subjects experienced headaches.
Solution :
a). The test is a left tailed test.
b). The sample proportion is :
[tex]$\hat p = \frac{x}{n}$[/tex]
[tex]$\hat p = \frac{17}{258}$[/tex]
= 0.065
Determining the Z statistics using the formula :
[tex]$Z=\frac{\hat p - p}{\sqrt{\frac{p(1-p)}{n}}}$[/tex]
[tex]$Z=\frac{0.065 - 0.11}{\sqrt{\frac{0.11(1-0.11)}{258}}}$[/tex]
= -2.31
∴ Z statistics value is -2.31
c). Using the excel function, the P-value is :
P-value = Normsdist(-2.31)
= 0.0104441
d). The null hypothesis is [tex]$H_0: P = 0.11$[/tex]
The level of significance is 0.01
We fail to reject the null hypothesis as the P value is less than or equal to the significant level.
Solve this inequality: 4x-8>-40
Answer:
x > - 8
Step-by-step explanation:
4x - 8 > - 40
4x > - 40 + 8
4x > - 32
Divide 4 on both sides,
4x / 4 > - 32 / 4
x > - 8
Value of x
1\5(x)(1/5)=6/3(5/1)
Answer:
1/25=3/30
1250=
2501
2389
5552
The point p=(2/5,y) lies on the unit circle below what is the value of y in simplest form
Step-by-step explanation:
distance of (1,0) from the origin is,
√{(1-0)²+(0-0)²}
= √1
= 1
So the radius of the circle is 1,
now for the point (2/5,y) distance from origin should be the same since it's the radius
so,
√{(2/5-0)²+(y-0)²} = 1
or, √(4/25+y²)=1
or, 4/25+y²=1
or, y² = 1-4/25
or, y²=21/25
or, y=√(21/25)
or, y=√21/5
so, the simplest form of y is,
[tex] \frac{ \sqrt{21} }{5} [/tex]
The vertex form of the equation of a vertical parabola is given by , where (h, k) is the vertex of the parabola and the absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to the directrix. You will use the GeoGebra geometry tool to create a vertical parabola and write the vertex form of its equation. Open GeoGebra, and complete each step below. If you need help, follow these instructions for using GeoGebra. Mark the focus of the parabola you are going to create at F(6, 4). Draw a horizontal line that is 6 units below the focus. This line will be the directrix of your parabola. What is the equation of the line?
Part F
What is the value of p for your parabola?
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Part G
Based on your responses to parts C and E above, write the equation of the parabola in vertex form. Show your work.
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Part H
Construct the parabola using the parabola tool in GeoGebra. Take a screenshot of your work, save it, and insert the image below.
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Characters used: 0 / 15000
Part I
Once you have constructed the parabola, use GeoGebra to display its equation. In the space below, rearrange the equation of the parabola shown in GeoGebra, and check whether it matches the equation in the vertex form that you wrote in part G. Show your work.
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Part J
To practice writing the equations of vertical parabolas, write the equations of these parabolas in vertex form:
focus at (-5, -3), and directrix y = -6
focus at (10, -4), and directrix y = 6.
Answer:
Step-by-step explanation:
Focus: (6,4)
Directrix lies 6 units below the focus, so the parabola opens upwards and focal length p = 6/2 = 3.
The equation of the directrix is y = -2.
The vertex is halfway between focus and directrix, at (6,1).
Equation of the parabola:
y = (1/(4p))(x-6)²+1 = (1/12)(x-6)²+1
The equation of the parabola is [tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]
What are parabolas?Parabolas are used to represent a quadratic equation in the vertex form
The given parameters are:
Focus = (6,4)
Directrix (x) = 6 units below the focus,
Start by calculating the focal length (p)
[tex]p = \frac x2[/tex]
This gives
[tex]p = \frac 62[/tex]
[tex]p = 3[/tex]
Next, calculate the vertex as follows:
[tex](h,k) = (6,2/2)[/tex]
Simplify
[tex](h,k) = (6,1)[/tex]
The equation of the parabola is then calculated a:
[tex]y = \frac{1}{4p}(x - h)^2 + k[/tex]
So, we have:
[tex]y = \frac{1}{4*3}(x - 6)^2 + 1[/tex]
Simplify
[tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]
Hence, the equation of the parabola is [tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]
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Which equation shows a slope of 3 and a y-intercept of (0,7)?
y = 7x + 3
y = −7x + 3
y = 3x
y = 3x + 7
Answer:
[tex]{ \tt{y = 3x + 7}}[/tex]
Step-by-step explanation:
General equation of a line:
[tex]{ \boxed{ \bf{y = mx + c}}}[/tex]
m is the slope, and c is the y-intercept:
m = 3, and c = 7
You are trying to get an important customer order out the door, but your boss keeps coming over to ask you about the status of this order and several other orders. He's just nervous and wants to be
Look at the image for the question?
Answer:
Surface area = the sum of the area of all six sides:
(11 · 10) + (11 · 10) + (11 · 8) + (11 · 8) + (8 · 10) + (8 · 10)
= 110 + 110 + 88 + 88 + 80 + 80
= 220 + 176 + 160
= 556 ft²
Answer:
556 ft^2
Step-by-step explanation:
The surface area of a rectangular prism is
SA = 2(lw+wh+lh) where h is the height l is the length and w is the width
SA = 2( 11*10+10*8+11*8)
= 2(110+80+88)
=2(278)
=556 ft^2
With a two dimensional surface, if we take (2, 1) as the center point and consider
a transformation with a rotation angle of 45◦, then point (3, 3) is transformed
into point (----)?
Answer:
Step-by-step explanation:
Distance between (2,1) and (3,3) = √5
parametric equations for circle of radius √5, centered at (2,1):
x = √5cosθ+2
y = √5sinθ+1
At (3,3), θ = arccos(1/√5) ≅ 63.4°
After 45° transformation:
θ' = 63.4° + 45° = 108.4°
x' = √5cos(108.4°)+2 = 1.29
y' = √sin(108.4°)+1 = 3.12
(3,3) transformed to (1.29,3.12)
PQRS is a parallelogram of area 18 cm. if PQ = 5 cm & QR = 4 cm. calculate the lengths of corresponding heights ?
Answer:
2cm
Step-by-step explanation:
area of parallelogram=b*h=18cm
5*4=20
length of corresponding heights=20-18
=2cm
the length of corresponding height of the parallelogram is : 2cm
Meaning of a parallelogramA parallelogram can be defined as a simple quadrilateral that is it possesses four sides and two pairs of parallel sides.
A opposite sides of a parallelogram are equal and the opposite angles of a parallelogram are equal.
In conclusion, the length of corresponding height of the parallelogram is : 2cm
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What is the constant of proportionality between y and x in the graph?
Answer:
4
Step-by-step explanation:
Constant of proportionality refers to the slope of the line in this case, the slope of the line is (4-0)/(1-0)=4
help me by using formula how did came by reason
Answer:
angleABC=isosceles triangle
angleB=(180-50)÷2=65
angle B=angleX(alternative angle)
angleB=65degree
Find the area AND perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answer:
a=40+8pi, p=4pi+4(sqrt of 29)
Step-by-step explanation:
rsm geometry class 122?
Please find the volume
Answer:
27/4 units^3
Step-by-step explanation:
V= area of the base × length
V= 3 3/8 × 2
= 27/4 units^3
Answer:
6 1/4 units ^3
Step-by-step explanation:
The volume is given by
V = Bh where B is the area of the base and h is the height
V = 3 3/8 *2
Changing to improper fractions
V = (8*3+3)/8 *2
= 27/8 *2
= 27 * 2/8
=27/4
Changing back to a mixed number
= 6 1/4
!!I NEED THE ANSWER PLS!!
Which of the following represents the divisor and the dividend for the
synthetic division problem below?
- 3/ 2 4 -4 6
A. -3 and -2x2 - 4x2 + 4x-6
B. x+3 and -2x2 - 4x +47-6
C. X+3 and 2x + 4x2 - 4x+6
D. *-3 and 2x2 + 4x2 - 4x+6
Answer:
B
Step-by-step explanation:
B . x+3 and -2x2 - 4x +47-6
B . x+3 and -2x2 - 4x +47-6
The divisor and the dividend for the given synthetic division problem are : [tex]x+3[/tex] and [tex]2x^3+4x^2-4x+6[/tex]
What is synthetic division?"It is a way of dividing one polynomial by another polynomial of first degree."
What is dividend?"The value that is divided by another value to get the result. "
What is divisor?"The value that divides another number either completely or with a remainder."
For given question,
We have been given a synthetic division problem.
- 3/ 2 4 -4 6
We need to represent the divisor and the dividend for the given synthetic division problem.
We know that, to perform synthetic division, here are the steps:
- The leading coefficient of the divisor should also be 1.
- Express the dividend in standard form.
- Write the leading coefficient in the dividend.
- Place the product of the number you brought down and the number in the division box in the preceding column.
- Write the result at the bottom of the row.
So, the divisor of the given synthetic division form would be,
x - (-3) = x + 3
And the dividend of the given synthetic division form would be,
There are four leading coefficient.
This means the dividend polynomial must be of degree 3.
From the leading coefficients 2 4 -4 6
[tex]2x^3+4x^2-4x+6[/tex]
Therefore, the divisor and the dividend for the given synthetic division problem are : [tex]x+3[/tex] and [tex]2x^3+4x^2-4x+6[/tex]
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Sarah has two similar rectangular boxes. The dimensions of Box 1 are four times those of Box 2.
How many times greater is the surface area of Box 1 than the surface area of Box 2?
8
64
4
16
Answer:
16
Step-by-step explanation:
an area is always calculated by multiplying 2 dimensions.
when changing the dimensions, then the change factors for EACH dimension go into the calculation too.
therefore, when both dimensions of an area are enlarged 4 times, then the area is enlarged 4×4 = 16 times.
this just propagates to the whole surface area of an object, as each individual area of the overall surface area is enlarged by the same factor. and so, the sum of all the individual areas (= altogether the surface area of the object) is also enlarged in total by the same factor.
just think
16×a + 16×b + 16×c ... = 16×(a+b+c+...)
and you understand why.
Identify the triangle, ABC, which has a 72∘ angle and a 36∘ angle.
Answer:
isosceles acute
Step-by-step explanation:
sum of angles in a triangle = 180
to find third angle, subtract 72 & 36 from 180 and you get 72
72, 36, and 72 are all less than 90 so it will be an acute triangle
It will also be isosceles bc there are 2 angles of the same measure
Is x - 0.30x equivalent to 0.70x?
hi
it's equal to as X = 1X
so 1X-0.3X = 0.7X
Answer:
yes
Step-by-step explanation:
as
x - 0.3x = 1×x - 0.3x = (1-0.3)x = 0.7x
graph the inaquality 16>_w
Answer:
A graph is below.
Step-by-step explanation:
How many more cherry pies have 60 to 89 cherries than 90 to 119 cherries?
Answer:
6 pies
Step-by-step explanation:
For 60 - 89 cherries there are 10 pies
For 90 -119 cherries there are 4 pies
10 -4 = 6
There are 6 more pies in the 60 -89 cherries category than in the 90-119 category
Find the value of x.
x
9
9
7
x = [?]
Answer:
14
Step-by-step explanation:
Describe how to find the domain of a square root function just by looking at the function.
Answer:
Step 1: Set the expression inside the square root greater than or equal to zero. Step 2: Solve the equation found in step 1. In this case, we divided by a negative number, so had to reverse the direction of the inequality symbol. Step 3: Write the answer using interval notation.
