Sarah sold her stock for $56.25 A share, which reflected a ROI of 7.7%. What was the original price of her stock?
graph the function for the given domain. y=2x D:{ -2,0,2,4}
We want to graph the given function for the given domain.
The graph can be seen at the end of the answer.
The given function is:
y = 2*x
The given domain is D: {-2, 0, 2, 4}
To graph this, we need to evaluate the function in the given values of the domain, we will get four points.
y = 2*(-2) = -4
Then we have the point (-2, -4)
y = 2*0 = 0
Then we have the point (0, 0)
y = 2*2 = 4
Then we have the point (2, 4)
y = 2*4 = 8
Then we have the point (4, 8)
Then we need to graph these four points, the graph can be seen below:
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Mika’s gym allows her to bring 3 guests for free. After the first three, she must pay $7 per guest. How many guests, g, can she bring to the gym if she pays $42? Three of these equations give the correct value of g. Which equation does NOT?
7g = 63
7(g – 3) = 42
7g – 3 = 42
g = 9
Answer:
[tex]7\cdot g-3 = 42[/tex]
Step-by-step explanation:
As the first three guest are three and each aditional guest costs $ 7 dollars. The formula is presented as follows:
[tex]7\cdot (g-3) = 42[/tex]
Or:
[tex]7\cdot g = 63[/tex]
Or:
[tex]g = 9[/tex]
The wrong equation is:
[tex]7\cdot g-3 = 42[/tex]
a. If m<7 = 37 , what is in m<4 ?
b. If m<7 = 37 , what is in m<2 ?
c. Describe the relationship between <4 and <8 .
d. Describe the relationship between <3 and <5 .
Answer:
a). m∠4 = 143°
b). m∠2 = 37°
c). ∠4 ≅ ∠8
d). ∠3 + ∠5 ≅ 180°
Step-by-step explanation:
a). Given m∠7 = 37°
Since m∠7 ≅ m∠6 [Vertically opposite angles]
and m∠6 + m∠4 = 180° [Sum of interior angles formed by parallel lines l, m and transverse.]
Therefore, 37°+ m∠4 = 180°
m∠4 = 180 - 37
= 143°
b). Since m∠6 ≅ m∠2 [Corresponding angles]
and m∠6 ≅ m∠7 [Vertically opposite angles]
Therefore, m∠2 ≅ m∠6 ≅ m∠7 ≅ 37°
c). ∠4 ≅ ∠8 [Corresponding angles]
d). ∠3 + ∠5 ≅ 180° [Interior angles of parallel lines m, l and a transverse].
Cameron is designing a calendar as a fund-raising project for math class. The cost of printing is $500, plus $2.50 per calendar. Write an equation in slope-intercept form that models the total cost of printing the calendars. Cameron estimates that the math class will sell 200 calendars. What will the total cost be?
The Graduate Record Examinations are widely used to help predict the performance of applicants to graduate schools. The range of possible scores on a GRE is 200 to 900. The psychology department at a university finds that the scores of its applicants on the quantitative GRE are approximately normal with mean = 544 and standard deviation = 103. Use your calculator or computer to find the relative frequency of applicants whose score X satisfies the following conditions: (As part of your answer, draw a standard normal curve and shade the area under the curve that represented the answer to the question; do this on scratch paper and provide a one-sentence description for the assignment).
X < 500
To find the relative frequency of applicants whose score X is less than 500 on the quantitative GRE, calculate the Z-score for 500 and find the corresponding area under the standard normal curve.
Explanation:To find the relative frequency of applicants whose score X is less than 500, we need to calculate the Z-score for 500. The formula for calculating the Z-score is: Z = (X - mean) / standard deviation. Plugging in the values, we get Z = (500 - 544) / 103 = -0.427.
Next, we need to find the corresponding area under the standard normal curve for the Z-score of -0.427. Using a calculator or a standard normal table, we find that the area to the left of -0.427 is approximately 0.3356.
Therefore, the relative frequency of applicants whose score is less than 500 is 0.3356, or 33.56%.
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A toy airplane costs $4.84.. It costs 4 times as much as a toy car. What is the cost of the toy car? Show your work.
Find m < 4 and m < 3
A bag contains 6 red balls and blue balls. 4 balls are selected at random. find the probability of selecting 4 red balls.
Another way is to note that there are (104)(104) (“10 choose 4”) ways to select 4 balls from a collection of 10. If 4 of those 10 balls are “special” in some way (in this case, “special” = “red”), then the number of ways to choose 4 special balls is (44)(44). (The factor of (60)(60) is included to convey that, after choosing 4 special balls, we choose none of the 6 non-special balls.) This line of reasoning gives the second expression.
. Earl purchased a living room set for $3,592 using a 12-month deferred payment plan. The interest rate after the introductory period is 21.80%. A down payment of $275 is required as well as a minimum monthly payment of $112. What is the balance after the introductory period if only the minimum payment is made until then?
Answer:
The required answer is $2839.25.
Step-by-step explanation:
[tex]112\times12=1344[/tex] dollars
Plus down payment = [tex]1344+275=1619[/tex] dollars
Now, compound interest is found as:
[tex]A=p(1+\frac{r}{n})^{nt}[/tex]
p = 3592
r = 21.80% or 0.2180
n = 12
t = 1
Substituting the values in formula:
[tex]A=3592(1+\frac{0.2180}{12})^{12}[/tex]
=> [tex]A=3592(1.018167)^{12}[/tex]
A = $4458.25
So, Balance = [tex]4458.25-1619=2839.25[/tex] dollars
Therefore, the required answer is $2839.25.
Are perfect square roots whole?
A cell phone service provider offers two plans. Plan A includes a fee of $25 per month and charges $0.25 for every call. Plan B includes a fee of $40 per month and offers unlimited calls. For what number of phone calls is the cost of plan B less than the cost of plan A?
more than 160 calls
more than 120 calls
more than 100 calls
more than 60 calls
PLEASE HELP!!
Write an equation in slope-intercept form of the line through point (6, –1) with slope m=4. Question 6 options: y + 1 = 4(x – 6) y = 4x – 1 y = 4x – 25 y + 6 = 4(x – 1)
The cooking time for a ham is 2/5 of an hour for each pound. A.) How long should you cook a ham that weighs 12 3/4 pounds? B.) Dinner time is 4:45 pm. What time should you start cooking the ham?
To cook a 12 3/4 pounds ham which requires 2/5 of an hour for each pound, it will take approximately 5.1 hours. If dinner is at 4:45 pm, you should start cooking around 11:39 am.
Explanation:The subject of your question is Mathematics. To solve this problem, let's understand first that the cooking time for a ham is 2/5 of an hour for each pound. This means that for each pound of ham, it should be cooked for 2/5 hour.
A.) To find how long you should cook a ham that weighs 12 3/4 pounds, you need to multiply that weight by 2/5. (12 3/4) * (2/5) ≈ 5.1 hours. So, you would need to cook the ham for approximately 5.1 hours.
B.) If dinner time is at 4:45 pm, and you know that the ham takes about 5.1 hours to cook, simply subtract 5.1 hours from the dinner time to find out when you should start cooking. 4:45pm - 5.1 hours ≈ 11:39am. Hence, you should begin cooking at around 11:39am to have the ham ready by 4:45pm.
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Which length is 10 6 times greater than a nanometer?
If the following two triangles are similar, find X.
Show work please
Giorgio surveyed 45 randomly selected shoppers at the mall and found that approximately 24% believe that the food court needs to be remodeled. To the nearest percent, with a confidence level of 99% (z*-score 2.58), what is the confidence interval for the proportion of shoppers who believe the food court needs to be remodeled? E = z* and C = + E
Answer with explanation:
Number of People Surveyed (S)= 45
Confidence Level = 99%
Percentage of population who believe that food court needs to be remodeled =24 %
→So, 24% of 45
[tex]=\frac{24}{100}\times 45=10.80[/tex]
= 11 people
Probability of population who thinks that food court needs to be remodeled(P)
[tex]=\frac{11}{45}[/tex]
[tex]Z_{99 percent}= 2.58[/tex]
Confidence level for a population is given by
[tex]=P \pm Z\sqrt{\frac{P*(1-P)}{S}}[/tex]
Substituting the values, of Z, P and S in above equation
[tex]=0.25\pm 2.58\sqrt{\frac{0.25*0.75}{45}}\\\\=0.25 \pm 2.58*0.064549\\\\=0.25 \pm 0.17\\\\= 0.25 - 0.17 , 0.25+0.17\\\\=0.08 , 0.42[/tex]
→→0.08 ≤proportion of shoppers who believe the food court needs to be remodeled≤0.42
→→8%≤proportion of shoppers who believe the food court needs to be remodeled≤42%
The expression (x2 + 16x + 64) – (x + 8)(x – 4) can be rewritten as k(x + 8). What is the value of k? k =
The value of k in the expression is 12.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To simplify the given expression, we first need to expand the second term using the distributive property:
(x + 8)(x - 4) = x² - 4x + 8x - 32 = x² + 4x - 32
Now we can substitute this expression into the original expression:
x² + 16x + 64 - (x² + 4x - 32)
Simplifying further, we can combine like terms:
12x + 96
Now we can see that the expression can be rewritten as:
12(x + 8)
So the value of k is 12.
Thus,
The value of k is 12.
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a dime has the circumference of about 56.27 millimeters. What is the radius of the dime? Round to two decimal places!
identify a pattern and find the next number in the pattern -0.8, -3.2, -12.8, -51.2
A:-358.4
B:-204.8
C:-51.2
D:4
The next number in the pattern -0.8, -3.2, -12.8, -51.2 is -204.8.
What is proportional relationship?A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
The numbers are -0.8, -3.2, -12.8, -51.2.
To find the pattern:
Divide the number to find the proportionate rate,
-3.2/-0.8 = 4
-12.8/-3.2 = 4
-51.2 /-3.2 = 4
So, the proportionality relationship is,
number = 4 x previous number.
So, the next number,
-51.2 x 4
= -204.8
Therefore, the number is -204.8.
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Solve the inequality. r + 4 – 2(r – 14) > 0
8 people are about to board a plane. In how many ways can this be done?
A small fair charges an admission fee for children and adults. The cost for admission is $3 per adult and $2 per child. On a certain day, total sales were $900, and 350 people attended the fair. How many children attended the fair that day? 80 children 150 children 200 children 320 children
Answer:
B. 150 children
Step-by-step explanation:
Let, number of children = x and number of adults = y.
Since, total number of people attended the fair are 350.
So, x + y = 350.
Moreover, charges per child is $2 and adult is $3.
As, total sales are given to be $900.
So, 2x + 3y = 900
Thus, we get the system of equations,
2x + 3y = 900
x + y = 350
We will now solve the equations,
x + y = 350 ⇒ y = 350 - x
So, 2x + 3y = 900 ⇒ 2x + 3(350 -x) = 900 ⇒ 2x + 1050 - 3x = 900 ⇒ -x = -150 ⇒ x = 150.
Then, y = 350 - x ⇒ y = 350 - 150 ⇒ y = 200.
Hence, number of children and adults that attended the fair are 150 and 200 respectively.
Using the formula r = d/t where d is the distance in miles, r is the rate, and t is the time in hours, at which rate must you travel to cover 337.5 miles in 4.5 hours?
Answer:
75 miles/hour
Step-by-step explanation:
Given information: d=337.5 miles and t=4.5 hours.
The given formula is
[tex]r=\frac{d}{t}[/tex]
where d is the distance in miles, r is the rate, and t is the time in hours.
We need to find the rate for d=337.5 miles and t=4.5 hours.
Substitute d=337.5 and t=4.5 in the above formula.
[tex]r=\frac{337.5}{4.5}[/tex]
[tex]r=75[/tex]
The value of r is 75, therefore we need to travel at the rate of 75 miles per hours to cover 337.5 miles in 4.5 hours.
What are the x and y-intercepts of the line described by the equation?
2x + 4y = 12.4
Enter your answers, in decimal form, in the boxes.
x-intercept = ____
y-intercept = _____
The x and y intercept of the given line is required,
The x intercept is [tex](6.2,0)[/tex]
The y intercept is [tex](0,3.1)[/tex]
The given line is [tex]2x+4y=12.4[/tex]
x intercept [tex]y=0[/tex]
[tex]2x+4\times 0=12.4\\\Rightarrow x=\dfrac{12.4}{2}\\\Rightarrow x=6.2[/tex]
The x intercept is [tex](6.2,0)[/tex]
y intercept [tex]x=0[/tex]
[tex]2\times 0+4y=12.4\\\Rightarrow y=\dfrac{12.4}{4}\\\Rightarrow y=3.1[/tex]
The y intercept is [tex](0,3.1)[/tex]
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Given right triangle ABC. To the nearest degree, find the measure of angle B.
Answer:
Step-by-step explanation:
We have the length of AC which is opposite angle B; we also have the length of the hypotenuse. We will use trig here to solve for angle B. The sin ratio is the one that fits.
sin(B) = side opposite / hypotenuse:
[tex]sin(B)= \frac{ 4.8}{ 5.1}[/tex] so
sin(B) = .9411764706
Now we will use the 2nd button on our calculators. This will give us the missing angle value. Press 2nd then sin and you will see on your screen:
[tex]sin^{-1 ([/tex]
Enter that decimal after the open parenthesis and hit "enter" to get
B = 70.25 or 70°
HELP please I have a bunch of these and I’m stressing cause I have like 50 tests tomorrow
Give three examples of when negative numbers are used in daily life
How many feet of fencing are need to enclose a triangular lot?
Use technology and the given confidence level and sample data to find the confidence interval for the population mean muμ. assume that the population does not exhibit a normal distribution. weight lost on a diet:weight lost on a diet: 99 % confidence 99% confidence n equals 61n=61 x overbar equals 2.0 kgx=2.0 kg s equals 4.8 kg
The given in this problem are:
99% confidence level
N = 61
Mean = 2.0 kg
Standard deviation = 4.8
Z value for a 9% confidence interval is 2.576
Confidence Interval = mean ± Z s/ sqrt n
= 2.0 ± 2.576(4.8/sqrt 61)
=2.0 ± 2.576 (0.6145770236779006736364371988794)
= 2.0 ± 1.5832
= 0.4168 < x < 3.5832