Answer:
B. 550
Step-by-step explanation:
550 is the smallest number that becomes 600 when rounded to the nearest hundred
Find an equation for the perpendicular bisector of the line segment whose endpoints are (8,9) and (4,−3).
x + 3y -15 = 0
Step-by-step explanation:
let (x,y) be the coordinate of bisector,
so (x,y) should be equal distance from point (8,9) and (4,-3)
(x-8)^2 + (y-9)^2 = (x-4)^2 + (y-(-3))^2
or, (x^2 - 16x + 64) + (y^2 - 18y + 81 )= (x^2 -8x + 16) + (y^2 + 6y + 9)
After cancelling x^2 and y^2 from both side, we get
-16x - 18y +145 = -8x +6y + 25
or, -16x + 8x - 18y - 6y +145 -25 = 0
or, -8x - 24y + 120 = 0
or -8 ( x + 3y - 15) = 0
or, x + 3y - 15 = 0 ------ this is the equation of the perpendicular bisector of line segment with endpoints (8,9) and (4,-3)
Jacob bought a magazine for $2.80 and three candy bars. Write an expression for how much Jacob paid.
Answer:
total = 2.8 + 3x
x is the price of the candy bars
A store surveyed their customers to find out their ages. The bar graph below shows the number of customers in each age group. What percent of customers surveyed were over 50%? Round your answer to 1 decimal place.
Bar graphs are used to represent data, where the vertical axis represents the frequency and the horizontal axis.
The percentage that is over 50 is 15.6%:
The data on the bar graph can be represented as:
Under 17 [tex]\to[/tex] 25
18 - 24 [tex]\to[/tex] 35
25 - 34 [tex]\to[/tex] 40
35 - 50 [tex]\to[/tex] 35
Over 50 [tex]\to[/tex] 25
So, the total customer surveyed are:
[tex]Total = 25 + 35 + 40 + 35 + 25[/tex]
[tex]Total = 160[/tex]
The percentage over 50 are:
[tex]\%Over\ 50 = \frac{Over\ 50}{Total } * 100\%[/tex]
[tex]\%Over\ 50 = \frac{25}{160} * 100\%[/tex]
[tex]\%Over\ 50 = 0.15625* 100\%[/tex]
[tex]\%Over\ 50 = 15.625\%[/tex]
Approximate
[tex]\%Over\ 50 = 15.6\%[/tex]
Read more at:
https://brainly.com/question/10440833
The polynomial p(x) = x3 – 7x - 6 has a known factor of (x + 1).
Rewrite p(x) as a product of linear factors.
p(x)
Hi there!
[tex]\large\boxed{(x -3)(x + 2)(x + 1)}[/tex]
We can use long division to find the other roots of p(x).
We know that x + 1 is a factor, so:
Set up:
Find how many times that the first term in the divisor goes into the first of the dividend. Subtract from like terms.
x² - x - 6
x + 1 | x³ + 0x² - 7x - 6
x³ + x²
0 - x² - 7x
- x² - x
0 - 6x - 6
-6x - 6
0 0
Therefore, x² - x - 6 is another factor. We can factor this further:
Find two numbers that add up to -1 and multiply into -6. We get:
-3, 2
(x - 3)(x + 2)
The entire polynomial factored is:
(x -3)(x + 2)(x + 1)
A committee on community relations in a college town plans to survey local businesses about the importance of students as customers. From the 10,000 businesses listed in the telephone book, the committee chooses 150 businesses at random. Of these, 72 return the questionnaire mailed by the committee. The nonresponse rate is ______ percent. (Give your answer as a whole number.)
Answer:
The nonresponse rate is 52 percent.
Step-by-step explanation:
150 sampled:
72 returned and 150 - 72 = 78
The nonresponse rate is
Percentage that 78 is out of 150, that is:
78*100%/150 = 52%
The nonresponse rate is 52 percent.
If f(×)=16×-30 and g(×)=14×-6, for which value of x does (f-g)(x)=0
Answer: [tex]x=12[/tex]
Step-by-step explanation:
[tex]f(x)=16x-30\\g(x)=14x-6[/tex] are the equations that you've given us.
Now if we plot these two equations on the graph we notice there's an intersection at (12,162). Therefore meaning that [tex]x=12[/tex].
We can prove that by doing the following calculations to prove that both sides are equal to each other.
The left side of the equal sign:
Step 1: Write the equation down:
[tex]16x-30[/tex]
Step 2: Substitute x for the numerical value we found.
[tex]16(12)-30[/tex]
Step 3: We will multiply [tex]16*20[/tex] first, giving us 192.
[tex]192-30[/tex]
Step 4: Subtract 192 from 30. Which gives us 162.
[tex]162[/tex]
The right side of the equal sign:
Step 1: Write the equation down:
[tex]14x-6[/tex]
Step 2: Substitute x for the numerical value we found.
[tex]14(12)-6[/tex]
Step 3: We will multiply [tex]14*12[/tex] first, giving us 168.
[tex]168-6[/tex]
Step 4: Subtract 168 from 6. Which gives us 162.
[tex]162[/tex]
We know that [tex]x=12[/tex] because when substituting x with 12, we get 162 on both sides. Therefore making this statement true and valid.
[tex]162=162[/tex]
Suppose you work for a political organization and you are interested in hearing how the residents of New York State feel about a particular issue. You are asked to create a sample of at least 10000 residents using a CLUSTER methodolgy. Explain how you could create this sample of New York State residents?
Since the state is broken up into counties, and each county subdivided into precincts, this provides a natural way to form cluster samples.
If the precinct populations are too large, then you can further subdivide based on household or building residence. In other words, you can randomly select a building and consider that a separate cluster. All residents of that building would be part of the cluster.
In cluster sampling, the idea is that whichever clusters you select, you survey every person who resides in that cluster. So naturally you need to be careful not to go overboard.
I will give brainliest if you answer properly.
Answer:
See below
Step-by-step explanation:
a)
[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]
[tex]\therefore x=\dfrac{4\pi }{3}[/tex]
But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution
Therefore,
[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]
This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.
Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]
b)
[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]
Once
[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]
As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]
[tex]\therefore x=-\dfrac{\pi }{6}[/tex]
c)
[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]
Therefore,
[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]
[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
The solutions are
[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
A certain marathon has had a wheelchair division since 1977. An interested fan wondered who is faster: the men's marathon winner or the women's wheelchair marathon winner, on average. A paired t-test was performed on data from a random selection of 15 of the marathons to determine if there was evidence to indicate that the women's winning wheelchair time is faster than the men's winning running time, on average. What must be true about the population of differences in the women's wheelchair winning times and men's winning times at this marathon for conclusions from the paired t-test to be valid? Choose the correct answer below. A. The distribution of sample means of the differences will be approximately normal if there are at least 30 years of data in the sample and/or if the population of differences in winning times for all years is normal. B. Because there were at least 5 years of observations, the distribution of sample means of the differences will be approximately normal by the Central Limit Theorem. C. Because the sample size is large enough, the distribution of differences for all years will be normal. D. Because of the small sample size of differences in winning times between the women's wheelchair winner and the men's running winner, the distribution of sample means of the differences cannot be normal.
Answer:
A. The distribution of sample means of the differences will be approximately normal if there are at least 30 years of data in the sample and/or if the population of differences in winning times for all years is normal.
Step-by-step explanation:
In other to perform a valid paired test, one of the conditions required is that, data for both groups must be approximately normal. To attain normality, the population distribution for the groups must be normal or based on the central limit theorem, the sample size must be large enough, usually n > 30. Hence, once either of the two conditions are met, the paired sample will be valid.
In a certain animal species, the probability that a healthy adult female will have no offspring in a given year is 0.24, while the probabilities of 1, 2, 3, or 4 offspring are respectively 0.25, 0.19, 0.17, and 0.15. Find the expected number of offspring.
Answer:
The expected number of offspring is 2
Step-by-step explanation:
The given parameters can be represented as:
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.24} & {0.25} & {0.19} & {0.17} & {0.15} \ \end{array}[/tex]
Required
The expected number of offspring
This implies that we calculate the expected value of the function.
So, we have:
[tex]E(x) = \sum x * P(x)[/tex]
Substitute known values
[tex]E(x) = 0 * 0.24 + 1 * 0.25 + 2 * 0.19+ 3 * 0.17 + 4 * 0.15[/tex]
Using a calculator, we have:
[tex]E(x) = 1.74[/tex]
[tex]E(x) = 2[/tex] --- approximated
Find the missing side lengths leave your answer as a racials simplest form
Answer:
x = 20
y = 10
it's a 30-60-90 triangle
A diameter perpendicular to a chord
that chord
Select one:
a. is parallel to
b. bisects
c. is equal to
Simplify the following by removing parentheses and combining terms
- (2x + 8) + 3(2x + 8) - 2x
Answer:
2x+16
Step-by-step explanation:
PEMDAS
SOMEONE PLEASE HELP ME!!!!!!!!
9514 1404 393
Answer:
PQ = 46
Step-by-step explanation:
Midsegment ST is half the length of base segment PQ.
2×ST = PQ
2×(5x -22) = 3x +19
10x -44 = 3x +19 . . . . . . . eliminate parentheses
7x = 63 . . . . . . . . . . . . add 44-3x
x = 9 . . . . . . . . . . . . divide by 7
PQ = 3x +19 = 3×9 +19
PQ = 46
A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 101 feet and the radius of the hemisphere is r feet. Express the volume of the silo as a function of r.
Answer:
[tex]V(r) =101\pi r^2 + \frac{2}{3}\pi r^3[/tex]
Step-by-step explanation:
Given
Shapes: cylinder and hemisphere
[tex]h = 101[/tex] --- height of cylinder
Required
The volume of the silo
The volume is calculated as:
Volume (V) = Volume of cylinder (V1) + Volume of hemisphere (V2)
So, we have:
[tex]V_1 = \pi r^2h[/tex]
[tex]V_1 = \pi r^2 * 101[/tex]
[tex]V_1 = 101\pi r^2[/tex] --- cylinder
[tex]V_2 = \frac{2}{3}\pi r^3[/tex] ---- hemisphere
So, the volume of the silo is:
[tex]V =V_1 + V_2[/tex]
[tex]V =101\pi r^2 + \frac{2}{3}\pi r^3[/tex]
Write as a function
[tex]V(r) =101\pi r^2 + \frac{2}{3}\pi r^3[/tex]
Where: [tex]\pi = \frac{22}{7}[/tex]
An advertiser goes to a printer and is charged $36 for 80 copies of one flyer and $46 for 242 copies of another flyer. The printer charges a fixed setup cost plus a charge for every copy of single-page flyers. Find a function that describes the cost of a printing job, if xx is the number of copies made.
Answer:
ytre
Step-by-step explanation:
A plane traveled 4425 miles with the wind in 7.5 hours and 3675 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind
Answer:
540 miles/hr and 50 miles/hr respectively
Step-by-step explanation:
Let the speed of plane in still air be x and the speed of wind be y.
ATQ, (x+y)*7.5=4425 and (x-y)*7.5=3675. Solving it, we get x=540 and y=50
Convert 653 in base 7 to base 10
300-20+100 divided by 4=
Answer:
95
Step-by-step explanation:
300-20=280
280+100=380
380÷4=95
There you go...
Consider the expressions 7y + 5 − 3 and 7y + 2. Which statement is true?
Answer:
A.
Step-by-step explanation:
Start with
7y + 5 - 3
Combine like terms:
7y + 2
By combining like terms in 7y + 5 - 3, we end up with 7y + 2 which is the second expression.
Therefore, the expressions are equivalent because they evaluate to equal values for every value of y.
Answer: A.
Probability that a person is chosen at random
Answer:
152 / 370
Step-by-step explanation:
Total number of people
152+218 = 370
P( own a dog) = people said yes / total
= 152 / 370
Solve for x.
2(3x - 7) = 16
Simplify your answer as much as possible.
X =
Answer:
x = 5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
2(3x - 7) = 16
Step 2: Solve for x
[Division Property of Equality] Divide 2 on both sides: 3x - 7 = 8[Addition Property of Equality] Add 7 on both sides: 3x = 15[Division Property of Equality] Divide 3 on both sides: x = 5Answer:
X=5
Step-by-step explanation:
divide by 2 on both sides first then you have
3x-7 = 8
take 7 to the other side so that you have an X factor on one side, thus
3x =15
then divide by 3 to remain with X
X = 5
A certain standardized test measures students’ knowledge in English and math. The English and math scores for 10 randomly selected students are given in the table.Using technology, what is the correlation coefficient?
0.68
0.83
0.91
0.95
Answer:
The answer is C
.91
ED2021
What is the Square root of 30 ,12,36
Answer:
the square root of:
30: 5.477225575
12: 3.464101615
36: 6 <-- explanation of square root: any number that when multiplied by itself equals your wanted number (in this case 36) will be the square root of your wanted number.
The answer to this question please.
Answer:
Part A) y=1,100x + 4,500
Part B) 14,400
Step-by-step explanation:
Part A)
There is a base fee of $4,500, meaning that the line begins at y=4500 (i.e. The y-intercept is [0,4500], so 'b' in y=mx+b is 4,500). There is a $1,100 hourly rate, which is proportional to the value of x, the amount of hours filmed. Therefore, 'm' in y=mx+b is $1,100.
Thus, the final equation looks like:
y= 1,100x + 4,500
Part B)
x=9
y=1,100x+4,500
y=1,100(9)+4,500
y=9,900+4,500
y=14,400
The following data represent the chemistry grades for a random sample of 12 freshmen at a certain college along with their scores on an intelligence test administered while they were still seniors in high school.
Test Chemistry Student Score,
x Grade, y
1 2 3 4 5 6 7 8 9 10 11 12 65 50 55 65 55 70 65 70 55 70 50 55 85 74 76 90 85 87 94 98 81 91 76 74
Compute and interpret the sample correlation coefficient.
Answer:
R = 0.862
Strong positive relationship
Step-by-step explanation:
Given the data:
Test Chemistry Student Score,
x Grade, y
1 2 3 4 5 6 7 8 9 10 11 12
Score,x = 65 50 55 65 55 70 65 70 55 70 50 55
Grade, y = 85 74 76 90 85 87 94 98 81 91 76 74
Using technology :
The CORREL function in excel, calculators will give accurate value of the correlation Coefficient between two variables, x and y. The correlation Coefficient obtained using technology is : 0.862
The correlation Coefficient value ranges between (-1 and 1) with values closer to either - 1 or 1 reflecting stronger relationship. A value of 0 means there is no relationship between the variables. Negative values indicate negative relationships while positive indicates positive association between the variables.
Therefore. With a correlation Coefficient of 0.862, the correlation Coefficient can be interpreted as meaning that ; there is a strong positive relationship between score and grade.
six times the sum of a number and 4 is 5
The sum of 6 times a number and 4 equals 5
The sum (+) of 6 times (multiply by 6) a number (x) and 4 equals (=) 5
6 times (multiply by 6) a number (x) + 4 = 5
6x + 4 = 5
6x = 5 - 4
6x = 1
x = 1/6
Answer:
6(x+4) = 5
=> 6x + 24 = 5
=> 6x= -19
=> x = -19/6
=> x = -3.16666
Lets subtitute the value of x for proof
6(x+4)
6(-3.16666+4)
-18.999996+24
= 5.00004~ 5.00
P is inversely proportional DY. IF P=1.2=when y=100, calculate
a the value of p when y=4
b the value of y when p=3
Answer:
a. P = 30
b. Y = 40
Step-by-step explanation:
Given the following data;
P = 1.2
Y = 100
First of all, we would have to determine the constant of proportionality;
P = k/Y (inverse proportion or relationship)
1.2 = k/100
k = 1.2 * 100
k = 120
a. To find the value of p when y = 4;
P = k/Y
P = 120/4
P = 30
b. To find the value of y when p = 3;
P = k/Y
Y = k/P
Y = 120/3
Y = 40
find the angle and area of shaded region
Area of shaded region = 1/2(πr²)
= 1/2(22/7×3×3)
= 99/7
= 99/7×2
= 198/7 cm^2
Thats the total area of the shaded region
Must click thanks and mark brainliest
IF A= -35 , B = 10 , C= -5 verify that:-
a x (b+c) = a x b + a x c
Plz tell
Answer:
see below
Step-by-step explanation:
a x (b+c) = a x b + a x c
Let A= -35 , B = 10 , C= -5
-35 * ( 10 -5) = -35 *10 + -35 * -5
-35 *(5) = -350 + 175
-175 = -175
