Answer:
B. (f - g)(x) = -3x² - x - 4
Step-by-step explanation:
→Set it up like so:
(-4x² - 6x - 1) - (-x² - 5x + 3)
→Distribute the -1 to (-x² - 5x + 3):
-4x² - 6x - 1 + x² + 5x - 3
→Add like terms (-4x² and x², -6x and 5x, -1 and -3):
-3x² - x - 4
3. In 28 days, a person saved $42. What was this person's
average daily savings?
Answer:
The average would be 42 / 28 = $1.50 / day.
Answer:
$1.50 per day
Step-by-step explanation:
Take the dollar amount and divide by the number of days
42 dollars / 28 days
1.50 dollars per day
$1.50 per day
What is the midpoint of the vertical line segment graphed below? (2,4) (2,-9)
Answer is A
Midpoint
[tex] \frac{x \: a xis}{2} . \frac{y \: axis}{2} [/tex]
[tex] \frac{2 + 2}{2} . \frac{4 + ( - 9)}{2} [/tex]
[tex](2. - 2.5 )[/tex]
Type your answers into the boxes.
There are 36 students in a class. The pie chart shows the colour of their hair.
Students' Hair Colours
40°
Red
Blonde
Dark
240°
How many students have blonde hair?
How many students have dark hair?
How many students have red hair?
Answer:
(a)24
(b)8
(c)4
Step-by-step explanation:
Number of STudents in the Class = 36
Angle representing Students with Red Hair =40 degrees
Angle representing Students with Blonde Hair =240 degrees
Therefore:
(a)Number of Students with Blonde Hair
[tex]=\dfrac{240^\circ}{360^\circ} \times 36\\\\ =24$ students[/tex]
(b)Number of Students with Dark Hair
Angle representing students with dark hair = 360-(240+40)=80 degrees
Therefore:
Number of Students with Dark Hair
[tex]=\dfrac{80^\circ}{360^\circ} \times 36\\\\ =8$ students[/tex]
(c)Number of Students with Blonde Hair
[tex]=\dfrac{40^\circ}{360^\circ} \times 36\\\\ =4$ students[/tex]
There are 8 students that have blond hair
There are 24 students that have dark hair
There are 4 students that have red hair
Please find attached the pie chart used in answering this question
A pie chart is a graph that displays information in a circle. The circle is divided into slices which represent a numerical proportion. The sum of angles in a pie chart is 360 degrees
To determine the number of students with a type of hair, use this formula :
(degree of the slice that represents the hair type / 360) x total number of students in the class
Degree of the slice that represents blond hair = 360 - (240 + 40) = 80
Students that have blonde hair = [tex]\frac{80}{360}[/tex] x 36 = 8
Students that have dark hair = [tex]\frac{240}{360}[/tex] x 36 = 24
Students that have red hair = [tex]\frac{40}{360}[/tex] x 36 = 4
To learn more about pie charts, please check : https://brainly.com/question/11433309?referrer=searchResults
Dominique is thinking about buying a hosue for 286000
Answer:
is this supposed to be a question?
Answer:
yah so
Step-by-step explanation:
Please answer I need help!
Answer:
c & d
Step-by-step explanation:
the description matches the information in the table
Answer: A, B, C
Step-by-step explanation:
domain = x
range = y
What’s the correct answer for this question?
Answer:
C:
Step-by-step explanation:
Both angles add up to 180°
<BCG + <BFG = 180°
2x+146+4x+238=180
6x+384 = 180°
6x = 180-384
6x = -204
Dividing both sides by 6
x = -34
What’s the correct answer for this question?
Answer: 3/20
Step-by-step explanation:
p(A)=the day selected in Monday =1/5
p(B)=student is absent
P(A∩B)=it is Monday AND a student is absent =3/100
Events A and B are independent so
P(A∩B) = P(A) · P(B)
3/100=1/5*p(B)
p(B)=3/20
The Tennessean, an online newspaper located in Nashville, Tennessee, conducts a daily poll to obtain reader opinions on a variety of current issues. In a recent poll, readers responded to the following question: "If a constitutional amendment to ban a state income tax is placed on the ballot in Tennessee, would you want it to pass?
Required:
a. What was the sample size for this poll?
b. Are the data categorical or quantitative?
c. Would it make more sense to use averages or percentages as a summary of the data for this question?
d. Of the respondents, 67% said Yes, they would want it to pass. How many individuals provided this response?
Answer:
Answers below
Step-by-step explanation:
a. What was the sample size for this poll?
b. Are the data categorical or quantitative?
c. Would it make more sense to use averages or percentages as a summary of the data for this question?
d. Of the respondents, 67% said Yes, they would want it to pass. How many individuals provided this response?
in a survey of more than 3000 people 93% of the respondents claimed to prefer Isaac's immaculate ice cream over any other brand of ice cream. which of the folloling groups were surveyed.
Answer:
The answer is 2,790.
Step-by-step explanation:
Here's a handy tool.
93% of 1 = 0.93 93% of 131 = 121.83 93% of 261 = 242.73 93% of 391 = 363.63
93% of 2 = 1.86 93% of 132 = 122.76 93% of 262 = 243.66 93% of 392 = 364.56
93% of 3 = 2.79 93% of 133 = 123.69 93% of 263 = 244.59 93% of 393 = 365.49
93% of 4 = 3.72 93% of 134 = 124.62 93% of 264 = 245.52 93% of 394 = 366.42
93% of 5 = 4.65 93% of 135 = 125.55 93% of 265 = 246.45 93% of 395 = 367.35
93% of 6 = 5.58 93% of 136 = 126.48 93% of 266 = 247.38 93% of 396 = 368.28
93% of 7 = 6.51 93% of 137 = 127.41 93% of 267 = 248.31 93% of 397 = 369.21
93% of 8 = 7.44 93% of 138 = 128.34 93% of 268 = 249.24 93% of 398 = 370.14
93% of 9 = 8.37 93% of 139 = 129.27 93% of 269 = 250.17 93% of 399 = 371.07
93% of 10 = 9.30 93% of 140 = 130.20 93% of 270 = 251.10 93% of 400 = 372.00
Of the mathematics degrees awarded in recent years, 76% were bachelor’s degrees, 21% were master’s degrees and the remaining 3% were doctorates. Moreover, women earned 52% of bachelors, 40% of masters and 22% of doctorates. What is the probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman? Give your answer to 4 decimal places.
Answer:
0.1729 = 17.29% probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Given to a woman.
Event B: Masters degree.
21% were master’s degrees
This means that [tex]P(B) = 0.21[/tex]
Women earned 40% of masters
This means that [tex]P(A|B) = 0.4[/tex]
Probability of the degree being given to a women:
52% of 76%, 40% of 21% and 22% of 3%. So
[tex]P(A) = 0.52*0.76 + 0.4*0.21 + 0.22*0.03 = 0.4858[/tex]
What is the probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman?
[tex]P(B|A) = \frac{0.21*0.4}{0.4858} = 0.1729[/tex]
0.1729 = 17.29% probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman
What is 11/12 divided 1/3
Answer:
2.75 or 2 3/4
Step-by-step explanation:
so here you use the recipricle of 1/3. so you would do 11/12 X 3/1 =33/12= 2 3/4
Answer: 11/4
Step-by-step explanation:
to divide a fraction by another, you multiply by the reciprocal(the opposite of a certain fraction). the reciprocal of 1/3 is 3/1. so:
[tex]\frac{11}{12} / \frac{1}{3} = \frac{11}{12} * \frac{3}{1} = \frac{33}{12} = \frac{11}{4}[/tex] (divide both sides by 3 to simplify for the last one)
Which of the following is(are) the solution(s) to | x-1|-8?
A. X= 7.-9
B. X = 9
C. X = -79
D. X = 7
Answer:
Step-by-step explanation:
|x-1|=8
if (x-1) >= 0 meaning x >= 1
then |x-1| = x-1
and then the solution of the equation is
x-1=8
<=> x = 9
if (x-1) <= 0 meaning x <= 1
then |x-1| = -(x-1) = -x+1
so the solution of the equation is
-x+1=8
<=> -x = 7
<=> x = -7
so the solutions are -7 and 9
answer C
do no hesitate if you need further explanation
thank you
Mariah spent $9.50 on 9 pounds of limes and pears. Limes cost $0.50 per pound and pears cost $1.50 per pound. Let l be the number of pounds of limes and let p be the number of pounds of pears.
The system of linear equations that models this scenario is:
l + p = 9
0.5l + 1.5p = 9.5
How many pounds of each type of fruit did she buy?
Answer:
4 pounds of lime and 5 pounds of pears
Step-by-step explanation:
I + P = 9
0.5l + 1.5P = 9.5
I = 9 - P
0.5(9 - P) + 1.5P = 9.5
4.5-0.5P + 1.5P = 9.5
4.5 + P (1P) = 9.5
P = 9.5-4.5 = 5
I = 9 - 5 = 4
Answer: 4 pounds of lime and 5 pounds of pears
16. Convert 55° to radians.
Answer:
0.96 radians
Step-by-step explanation:
Formula
1° = [tex]\frac{\pi }{180}[/tex] radians
Multiplying both sides by 55, It becomes
55° = [tex](\frac{\pi }{180} )*55[/tex]
55° = [tex]\frac{55\pi }{180}[/tex]
= 172.8/180
= 0.96 radians
Which choice is equivalent to the expression below?
root-81
A. 9i
B. i root9
C. root9i
D. -9
E. -root9
Answer: B
Step-by-step explanation:
Please answer this correctly
Answer:
326
Step-by-step explanation:
l x w
7x8
25x6
4x30
326
Find the volume of the cone below.
Answer:
[tex] V =\frac{1}{3} \pi r^2 h[/tex]
For this case we know that the radius is r=7cm and the height is h =11cm. And replacing we got:
[tex] V=\frac{1}{3} \pi (7cm)^2 (11cm)= \frac{1}{3} \pi (49cm^2) (11 cm)=\frac{539}{3} \pi cm^3[/tex]
And the best option would be:
[tex] V = \frac{539}{3} \pi cm^3 [/tex]
Step-by-step explanation:
For this case we know that the volume of the cone is given by:
[tex] V =\frac{1}{3} \pi r^2 h[/tex]
For this case we know that the radius is r=7cm and the height is h =11cm. And replacing we got:
[tex] V=\frac{1}{3} \pi (7cm)^2 (11cm)= \frac{1}{3} \pi (49cm^2) (11 cm)=\frac{539}{3} \pi cm^3[/tex]
And the best option would be:
[tex] V = \frac{539}{3} \pi cm^3 [/tex]
A 50 ft kite string is flying on the beach above an umbrella. You are holding the end
of the string and are 12 feet from the umbrella. How high in the air is the kite flying?
Round to the nearest degree.
Answer:
The height of the kite is 48.54 feet
The angle of elevation is 76.11°
Step-by-step explanation:
To find the height of the kite, we can use the Pythagoras' theorem in the triangle created by the length of the string (hypotenuse), the height of the kite and the distance to the umbrella (catheti).
Then, we have:
50^2 = 12^2 + height^2
height^2 = 2500 - 144
height^2 = 2356
height = 48.54 ft
So the kite is 48.54 feet high in the air.
The angle of elevation can be calculated using the cosine relation:
cos(angle) = 12 / 50
cos(angle) = 0.24
angle = 76.11°
What is the answerrrrrrrrrrrr :(((((((((((
Answer: The answer is choice 3
Step-by-step explanation:
i think the answer is c
Step-by-step explanation:
i don't think u would want a whole explanation
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 260.5-cm and a standard deviation of 1.6-cm. For shipment, 8 steel rods are bundled together.Find the probability that the average length of a randomly selected bundle of steel rods is greater than 260.2-cm.P(M > 260.2-cm) = Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Answer:
P(M > 260.2-cm) = 0.702
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 260.5, \sigma = 1.6, n = 8, s = \frac{1.6}{\sqrt{8}} = 0.5657[/tex]
P(M > 260.2-cm)
This is 1 subtracted by the pvalue of Z when X = 260.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{260.2 - 260.5}{0.5657}[/tex]
[tex]Z = -0.53[/tex]
[tex]Z = -0.53[/tex] has a pvalue of 0.298.
1 - 0.298 = 0.702
So
P(M > 260.2-cm) = 0.702
Accident rate data y1, ...., y12 were collected over 12 consecutive years t=1,2,...12. At over 12 consecutive years t = 1,2,..., 12. At the end of the 6th year, a change in safety regulations occured. FOr each of the following situations, set up a linear model of the form y=XB+E. Define X and B appropriately.
a. The accident rate y is a linear function of t with the new safety regulations having no effect.
b. The accident rate y is a quadratic function of t with the new regulations having no effect.
c. The accident rate y is a linear function of t. The slope for t>= 7 is the same as for t<7. However there is a discrete jump for t=7.
d. The accident rate y is a linear function of t. After t=7, the slope changes, with the two lines intersecting at t=7.
Answer:
The correct option is;
The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7
Step-by-step explanation:
The given parameters are;
Accident rate data = y₁, y₂, y₃, y₄, y₅, y₆, y₇, y₈, y₉, y₁₀, y₁₁, y₁₂
Time at which data was recorded = t₁, t₂, t₃, t₄, t₅, t₆, t₇, t₈, t₉, t₁₀, t₁₁, t₁₂
Accident rate equation is a linear model given as follows;
y = X·B + E
Where:
y = Accident rate
X = Slope of linear model
B = Year
E = y intercept of model
At the end of the 6th year, a change in a regulation that affects safety, hence accident rate occurred given as follows;
Before the change in safety regulations occurred for year t < 7 y₁ = X₁B + E₁
After the change in safety regulations occurred for year t < 7 y₂ = X₂B + E₂
Therefore the slope changes from X₁ to X₂ after t = 7 with the second linear model starting from the end of the first linear model making the two lines intersect at t = 7 (the beginning of year 7)
Hence the correct option is that "The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7."
A stack of 4 identical books is 6.28 high. What is the heigh of 30 of these books?
Answer:47.1
Step-by-step explanation:6.28/4=x/30
188.4=4x
47.1=x
Answer:
47.1
Step-by-step explanation:
height of 1 book=6.28÷4=1.57
height of 30 books=1.57×30=47.1
Tori needs to make some house repairs in three years that will cost $9,000. She has some money in an account earning 9% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs
Answer:
She needs to have approximately $6950 on that account.
Step-by-step explanation:
Since the account has an interest rate of 9% annually, then it's compounded and the earnings can be found by the following expression:
[tex]M = C*(1 + r)^t[/tex]
Where M is the final amount, C is the initial amount, r is the interest rate and t is the time elapsed in years.
She needs the money in 3 years, therefore t = 3. Applying this to the problem we have:
[tex]9000 = C*(1 + 0.09)^3\\9000 = C*(1.09)^3\\C*1.295 = 9000\\C = \frac{9000}{1.295}\\C = 6949.81[/tex]
She needs to have approximately $6950 on that account.
Quadrilateral BCDE is a kite. What is BF?
B
20
С
12
E
F
D
Answer:
32
Step-by-step explanation:
if u do pythagoras, sq root of 20^2-12^2=16
16x2=32
Eli uses 1/4 pound of apples to make 4 servings of fruit salad. He uses the same amount of apples for each serving. What amount of apples does he use for each serving of fruit salad?
Answer:
1/16 pound
Step-by-step explanation:
1/4 ÷ 4 = 1/4 x 1/4 = 1/16
If the measure of angle 2 is (5 x + 14) degrees and angle 3 is (7 x minus 14) degrees, what is the measure of angle 1 in degrees?
2 lines intersect to form 4 angles. From top left, clockwise, the angles are 1, 2, 3, 4.
88 degrees
89 degrees
90 degrees
91 degrees
Answer:
89 degrees
Step-by-step explanation:
The angle 1 is the same as angle 3.
Angle 2 is the same as angle 4.
The sum of these four angles is 360 degrees.
We have that:
Angle 2 = Angle 4 = 7x - 14
Angle 3 = Angle 1 = 5x + 14
Finding x:
Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360
2*(5x + 14) + 2*(7x - 14) = 360
10x + 28 + 14x - 28 = 360
24x = 360
x = 15
Angle 1:
5x + 14 = 5*15 + 14 = 89 degrees
Answer:
I think it is B
Step-by-step explanation:
Mathematics
ose the correct answer:
. What number should be added to (-5/16) to get ( 7/24)?
Answer:
0.6042 or 29/48
Step-by-step explanation:
-5/16 = -0.3125
7/24 = 0.2917
0.2917 - -0.3125 = 0.6042
0.6042 ≅ 29/48
Answer:
29/48
Step-by-step explanation:
-5/16 + x= 7/24
x= 7/24-(-5/16)
x=7/24+5/16
x= 2*7/2*24+ 3*5/3*16
x=29/48
During the late 1980s and the early 1990s the Pepsi Challenge was in full swing. During the challenge, participants were asked to taste cola from both Coke and Pepsi. Once they had tasted both drinks, the participants were asked to report which was better tasting. The results indicated that participants found Pepsi products to be better tasting. What is the dependent variable in this study? coruse hero psyc 255
Answer:
Taste
Step-by-step explanation:
In the challenge, participants were asked to taste cola from both Coke and Pepsi. They were to give a report on which of the two drinks tasted better.
The taste reported by the participants is dependent on the type of cola taken (either Coke or Pepsi).
Therefore, the taste is the dependent variable while the types of cola are the independent variables.
Maria, Daniel, Stephanie, Michael, Elena, Tyler, Sue, and Dimitri have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if Maria and Daniel are to sit next to each other?
Answer:
1x1x6x5x4x3x2x1 = 720 also they can sit in:
6x1x1x5x4x3x2x1 = 720
6x5x1x1x4x3x2x1 = 720
6x5x4x1x1x3x2x1 = 720
6x5x4x3x1x1x2x1 = 720
6x5x4x3x2x1x1x1 = 720
6x5x4x3x2x1x1x1 = 720 or you could have gone 720 x 7
The circular area covered by a cell phone tower can be represented by the expression 225π miles2. What is the approximate length of the diameter of this circular area
Answer:
The length of the diameter of this circular area is of 30 miles.
Step-by-step explanation:
The area of a circular region can be represented by the following equation:
[tex]A = \pi r^{2}[/tex]
In which r is the radius. The diameter is twice the radius.
In this question:
[tex]A = 225\pi[/tex]
So
[tex]A = \pi r^{2}[/tex]
[tex]225\pi = \pi r^{2}[/tex]
[tex]r^{2} = 225[/tex]
[tex]r = \pm \sqrt{225}[/tex]
The radius is a positive measure, so
[tex]r = 15[/tex]
Area in squared miles, so the radius in miles.
What is the approximate length of the diameter of this circular area
D = 2r = 2*15 = 30 miles
The length of the diameter of this circular area is of 30 miles.