Divide the amount off the price by the percentage off:
1.05 / 0.15 = 7
The original price is $7.00
help with this I don't know how to solve please and thanks
Answer:
6.5 ft
Step-by-step explanation:
When we draw out our picture of our triangle and label our givens, we should see that we need to use cos∅:
cos57° = x/12
12cos57° = x
x = 6.53567 ft
Can someone teach me how to solve this problem please:)
Answer:
x= -3, y= -5
or x= 5, y=3
Step-by-step explanation:
① Label the 2 equations
x² +y²= 34 -----(1)
3x -3y= 6 -----(2)
From (2):
x -y= 2 -----(3)
Notice that (x-y)²= x² -2xy +y²
Thus, (equation 3)²= (equation 1) -2xy
Squaring (3):
(x -y)²= 2²
(x -y)²= 4
Expand terms in bracket:
x² -2xy +y²= 4
x² +y² -2xy= 4 -----(4)
subst. (1) into (4):
34 -2xy= 4
2xy= 34 -4 (bring constant to 1 side)
2xy= 30 (simplify)
xy= 30 ÷2 (÷2 throughout)
xy= 15 -----(5)
From (3):
x= y +2 -----(6)
I'll rewrite 2 of the equations.
x= y +2 -----(6)
xy= 15 -----(5)
Subst. (6) into (5):
y(y+2)= 15
y² +2y= 15
y² +2y -15= 0
(y +5)(y -3)=0
y+5= 0 or y-3=0
y= -5 or y= 3
Subst. into (6):
x= -5 +2 or x= 3 +2
x= -3 or x= 5
Answer:
y=-5, y=3
x=-3., x=5
Step-by-step explanation:
x^2+y^2=34
3x-3y=6
isolate x in te equation
3x-3y=6
x=3/3 y+6/3
x=y+2
plug the y+2 in the equation:
x^2+y^2=34
(y+2)^2+y^2=34
y^2+4y+4+y^2=34
2y^2+4y=34-4
2y^2+4y=30 divide by 2
y^2+2x-15=0 factorize
(y+5)(y-3)=0 eiter y+5=0 ten y=-5 or y-3=0 then y=3
now plug the solution in the equation
3x-3y=6
3x-3(-5)=6
3x=6-15
x=-9/3=-3
for y=3
3x-3y=6
3x-9=6
3x=15
x=5
my dad is designing a new garden. he has 21 feet of fencing to go around the garden. he wants the length of the garden to be 1 1/2 feet longer than the width. how wide should he make the garden?
Answer:
21=2w+2w+3 18=4w w=4.5
Identify whether the given value is a discrete random variable, a continuous random variable, or if it is not a random variable:
1) A college basketball player's height that is reported in the game-day program
2) The color of a student's car
3) The exact weight of an airline passenger's carry-on bag
Answer:
1. continuous random variable
2. not a random variable
3. a continuous random variable
Step-by-step explanation:
The classifications are as follow
a) The height of the player reported in the game day program is treated as a continuous random variable as these values could be determined through measuring them
b) The color of student car is not a random variable as it does not contain any quantitative data or we can say numerical data
c) The exact weight of the bag is a continuous variable as it is lie between the range
Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 421 randomly selected adults showed that 65% of them would erase all of their personal information online if they could. Find the value of the test statistic.
Answer:
The statistic would be given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
And replacing we got:
[tex]z=\frac{0.65 -0.5}{\sqrt{\frac{0.5(1-0.5)}{421}}}=6.16[/tex]
Step-by-step explanation:
Information given
n=421 represent the random sample taken
[tex]\hat p=0.65[/tex] estimated proportion of adults that would erase all of their personal information online if they could
[tex]p_o=0.5[/tex] is the value that we want to test
z would represent the statistic
Hypothesis to test
We want to check if Most adults would erase all of their personal information online if they could, then the system of hypothesis are :
Null hypothesis:[tex]p\leq 0.5[/tex]
Alternative hypothesis:[tex]p > 0.5[/tex]
The statistic would be given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
And replacing we got:
[tex]z=\frac{0.65 -0.5}{\sqrt{\frac{0.5(1-0.5)}{421}}}=6.16[/tex]
From the information given, it is found that the value of the test statistic is z = 6.16.
At the null hypothesis, we test if it is not most adults that would erase all of their personal information online if they could, that is, the proportion is of at most 50%, hence:
[tex]H_0: p = 0.5[/tex]
At the alternative hypothesis, we test if most adults would, that is, if the proportion is greater than 50%.
[tex]H_1: p > 0.5[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.In this problem, the parameters are: [tex]p = 0.5, n = 421, \overline{p} = 0.65[/tex].
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.65 - 0.5}{\sqrt{\frac{0.5(0.5)}{421}}}[/tex]
[tex]z = 6.16[/tex]
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At the farm, corn costs $2.50 per pound. How much would 3 1/2 pounds of corn cost? Write your answer in dollars and cents.
Multiply price per pound by total pounds:
2.50 x 3.5 = 8.75
Total cost = $8.75
Answer:
The cost is $8.75 for 3.5 lbs
Step-by-step explanation:
The rate is 2.50 per pound
Multiply the number of pounds by the rate
3.5 * 2.50 =8.75
The cost is $8.75 for 3.5 lbs
Please help! V^2 = 25/81
Answer:
C and D
Step-by-step explanation:
khan acedemy
An equation is formed when two equal expressions. The solutions to the given equation are A, B, and C.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the given equation v²=25/81 can be found as shown below.
v²=25/81
Taking the square root of both sides of the equation,
√(v²) = √(25/81)
v = √(25/81)
v = √(5² / 9²)
v = ± 5/9
Hence, the solutions of the given equation are A, B, and C.
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A takeaway sells 10-inch pizzas and 12-inch pizzas.
The profit made in week 1 is 0.69 and week 2 is 0.71.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
A takeaway sells 10-inch pizzas and 12-inch pizzas.
From the table
For week 1:
Proportion= 509/ 736 = 0.69
and, week 2:
Proportion= 765/ 1076 = 0.71
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Find the area of a circle with a diameter of 8yards. Use 3.14. The area of the circle is approximate
Answer:
50.24 yd²
Step-by-step explanation:
pi r² = (3.14)(4)² = 50.24
An automobile manufacturer has given its car a 46.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 150 cars, they found a mean MPG of 46.5. Assume the population standard deviation is known to be 1.1. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
[tex]z=\frac{46.5-46.7}{\frac{1.1}{\sqrt{150}}}=-2.23[/tex]
The p value would be given by:
[tex]p_v =2*P(z<-2.23)=0.0257[/tex]
For this case since th p value is lower than the significance level of0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly different from 46.7 MPG
Step-by-step explanation:
Information given
[tex]\bar X=46.5[/tex] represent the mean
[tex]\sigma=1.1[/tex] represent the population standard deviation
[tex]n=150[/tex] sample size
[tex]\mu_o =46.7[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean for this case is 46.7, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 46.7[/tex]
Alternative hypothesis:[tex]\mu \neq 46.7[/tex]
Since we know the population deviation the statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{46.5-46.7}{\frac{1.1}{\sqrt{150}}}=-2.23[/tex]
The p value would be given by:
[tex]p_v =2*P(z<-2.23)=0.0257[/tex]
For this case since th p value is lower than the significance level of0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly different from 46.7 MPG
Profit Function for Producing Thermometers The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management estimates that the profit (in dollars) realizable by the company for the manufacture and sale of x units of thermometers each week is represented by the function below, where x ≥ 0. Find the interval where the profit function P is increasing and the interval where P is decreasing. (Enter your answer using interval notation.) P(x) = −0.004x2 + 6x − 5,000 Increasing: Decreasing:
Answer:
Increasing: [tex](0, 750)[/tex]
Decreasing: [tex](750, \infty)[/tex]
Step-by-step explanation:
Critical points:
The critical points of a function f(x) are the values of x for which:
[tex]f'(x) = 0[/tex]
For any value of x, if f'(x) > 0, the function is increasing. Otherwise, if f'(x) < 0, the function is decreasing.
The critical points help us find these intervals.
In this question:
[tex]P(x) = -0.004x^{2} + 6x - 5000[/tex]
So
[tex]P'(x) = -0.008x + 6[/tex]
Critical point:
[tex]P'(x) = 0[/tex]
[tex]-0.008x + 6 = 0[/tex]
[tex]0.008x = 6[/tex]
[tex]x = \frac{6}{0.008}[/tex]
[tex]x = 750[/tex]
We have two intervals:
(0, 750) and [tex](750, \infty)[/tex]
(0, 750)
Will find P'(x) when x = 1
[tex]P'(x) = -0.008x + 6 = -0.008*1 + 6 = 5.992[/tex]
Positive, so increasing.
Interval [tex](750, \infty)[/tex]
Will find P'(x) when x = 800
[tex]P'(x) = -0.008x + 6 = -0.008*800 + 6 = -0.4[/tex]
Negative, then decreasing.
Answer:
Increasing: [tex](0, 750)[/tex]
Decreasing: [tex](750, \infty)[/tex]
You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures: 44 32.8 59.2 31.4 12.7 68.5 84.7 72.5 55.7 Find the 98% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place). 98% C.I.
Answer:
[tex] 51.278 -2.896 \frac{22.979}{\sqrt{9}}= 29.096[/tex]
[tex] 51.278 +2.896 \frac{22.979}{\sqrt{9}}= 73.460[/tex]
And the interval would be:
[tex] (29.10 \leq \mu \leq 73.46)[/tex]
Step-by-step explanation:
For this problem we have the following dataset given:
44 32.8 59.2 31.4 12.7 68.5 84.7 72.5 55.7
We can find the mean and sample deviation with the following formulas:
[tex] \bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And replacing we got:
[tex]\bar X= 51.278[/tex]
[tex] s= 22.979[/tex]
The confidence interval for the mean is given by:
[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
The degrees of freedom are:
[tex] df=n-1= 9-1=8[/tex]
The confidence would be 0.98 and the significance [tex]\alpha=0.02[/tex] then the critical value would be:
[tex] t_{\alpha/2}= 2.896[/tex]
Ad replacing we got:
[tex] 51.278 -2.896 \frac{22.979}{\sqrt{9}}= 29.096[/tex]
[tex] 51.278 +2.896 \frac{22.979}{\sqrt{9}}= 73.460[/tex]
And the interval would be:
[tex] (29.10 \leq \mu \leq 73.46)[/tex]
ten percent of 140,000 = ?
Answer:
14000
Step-by-step explanation:
Of means multiply
10% * 140000
Change to decimal form
.10 * 140000
14000
Answer:
[tex]14000[/tex]
Step-by-step explanation:
[tex]10\% \times 140000[/tex]
[tex]\mathrm{Apply} \: a\% = \frac{a}{100}[/tex]
[tex]\frac{10}{100} \times 140000[/tex]
[tex]\mathrm{Apply} \: \frac{a}{100} \times b = \frac{ab}{100}[/tex]
[tex]\frac{1400000}{100}[/tex]
[tex]\mathrm{Simplify.}[/tex]
[tex]\frac{14000}{1} =14000[/tex]
The graphed line shown below is y = 3 x minus 1. On a coordinate plane, a line goes through (0, negative 1) and (1, 2). Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions? y + 1 = 3 x y = negative 3 x + 1 y = 3 x + 1 y minus 3 x = negative 3
Answer:
y + 1 = 3x
Step-by-step explanation:
In order for there to be an infinite number of solutions, the two lines need to be the same.
y+1 = 3x
y=3x-1 are both the same
Answer:
a)y + 1 = 3x
Step-by-step explanation:
Any polygon can be the base of a prism. A. True B. False
Answer:
true
Step-by-step explanation:
A prism is a solid with parallelogram sides (usually rectangles) and a polygon for the 2 bases. Any polygon can be the base.
Answer:
Hello!
__________________
Your answer would be (A) True.
Step-by-step explanation: Hope this helped you!
Any polygon can be the base of a prism so the answer is true.
By what percent will the fraction increase if its numerator is increased by 60% and denominator is decreased by 20% ?
Answer:
100%
Step-by-step explanation:
Start with x.
x = x/1
Increase the numerator by 60% to 1.6x.
Decrease the numerator by 20% to 0.8.
The new fraction is
1.6x/0.8
Do the division.
1.6x/0.8 = 2x
The fraction increased from x to 2x. It became double of what it was. From x to 2x, the increase is x. Since x was the original number x is 100%.
The increase is 100%.
Answer:
33%
Step-by-step explanation:
let fraction be x/y
numerator increased by 60%
=x+60%ofx
=8x
denominator increased by 20%
=y+20%of y
so the increased fraction is 4x/3y
let the fraction is increased by a%
then
x/y +a%of (x/y)=4x/3y
or, a%of(x/y)=x/3y
[tex]a\% = \frac{x}{3y} \times \frac{y}{x} [/tex]
therefore a=33
anda%=33%
What is 3 1/2 times 4?
Answer:
14
Step-by-step explanation:
3 1/2 × 4
Convert 3 1/2 to an improper fraction.
7/2 × 4
7/2 × 4/1
Multiply.
(7× 4) / (2 × 1)
28 / 2
= 14
Answer: 14
Step-by-step explanation: To multiply a mixed number times a whole number, first write each of them as an improper fraction.
So we can rewrite 3 and 1/2 as the improper fraction 7/2
and we can write 4 as the improper fraction 4/1.
If you've forgotten how to write a mixed number as an improper fraction, feel free to ask me below and I will review this with you.
So now we have 7/2 × 4/1.
When we're multiplying fractions, we want to
cross-cancel first whenever possible.
So here, notice that we can cross-cancel 2 and 4 to 1 and 2.
So we have 7/1 × 2/1.
Now we just multiply across the numerators and multiply across the denominators and we have our answer, 14/1 or just 14.
write the equation of a circle with the center (6,4) that passes through the coordinate (2,1) in your final answer include all of your calculations
Step-by-step explanation:
define define equation we need the value of the radius and
James plays at the neighborhood basketball court which is enclosed by a circular fence. The circle created by fence has a radius of 50 feet. What is the APPROXIMATE area of the space enclosed by the fence? Use 3.14 for π. 1,962.5 sq ft 7,850 sq ft 157.5 sq ft 314 sq ft
Answer:
7850 feet.sq
Step-by-step explanation:
the area of a cercle is:
A = r²*π where r is the radius
A= 50²*3.14 = 7850 ft²
g A CD player with an original price of $380.00 is on sale at 35% off. What is the discount amount and the CD player sale price?
Answer:
Cost: $247
Discount: $133
Step-by-step explanation:
Simply multiply 380 and 35% off together to get your answer:
380(1 - 0.35)
380(0.65)
247
To find the discount amount, simply subtract the 2 numbers to get your answer:
380 - 247 = 133
please please please please help i need to pass please
Answer:
D
Step-by-step explanation:
Solution:-
The standard sinusoidal waveform defined over the domain [ 0 , 2π ] is given as:
f ( x ) = sin ( w*x ± k ) ± b
Where,
w: The frequency of the cycle
k: The phase difference
b: The vertical shift of center line from origin
We are given that the function completes 2 cycles over the domain of [ 0 , 2π ]. The number of cycles of a sinusoidal wave is given by the frequency parameter ( w ).
We will plug in w = 2. No information is given regarding the phase difference ( k ) and the position of waveform from the origin. So we can set these parameters to zero. k = b = 0.
The resulting sinusoidal waveform can be expressed as:
f ( x ) = sin ( 2x ) ... Answer
You are ordering softballs for two softball leagues. The Elementary League uses a
larger softball priced at $2.75 each. The Middle School league uses a smaller softball
prices at $3.25 each. You order a total of 80 softballs for $245. What equations
would you use to find out how many of each size of softball you can order. Let L =
the larger softball and let S = the smaller softball.
Answer:L=30 S=50
Step-by-step explanation:
3.25 x 50 = 162.5
245 - 162.5 = 82.5
82.5 divided by 30 equals 2.75.
heres a list of numbers 3 6 9 7 4 6 7 0 7 Find median,mean,range and mode
median=order them and find the middle=6
mean=add them all up and divide by the amount of numbers=(3+6+9+7+4+6+7+0 +7)/9=5.4
range= the difference between the smallest and largest number=9-3=6
mode= the one that appears the most= 7
The median, mean, range and mode will be 6, 5.4, 9 and 7.
The median is the number in the middle when arranged in an ascending order. The numbers will be:
0, 3, 4, 6, 6, 7, 7, 7, 9.
The median is 6.
The range is the difference between the highest and lowest number which is: = 9 - 0 = 9
The mode is the number that appears most which is 7.
The mean will be the average which will be:
= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.
= 49/9
= 5.4
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Consider rolling dice and getting a total of 8. Find the probability if two dice are rolled. (Enter the value of probability in decimals. Round the answer to three decimal places.)
Answer:
13.89%
Step-by-step explanation:
The probability when two dices are rolled and their sum is 8 is shown below:
But before that we need to see the probabilities of the sum i.e 8
2 + 6 = 8
3 + 5 = 8
4 + 4 = 8
5 + 3 = 8
6 + 2 = 8
There are 5 outcomes
And, the two dice is 36 i.e square of 6
So, the probability of two dices are rolled and their sum is 8 is
= [tex]\frac{5}{36}[/tex]
= 13.89%
Find the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval. Leave your answer in terms of n, the number of subintervals. Function Interval f(x) = 7 − 2x [1, 2]
Answer:
-2n
Step-by-step explanation:
f(x)=7-2x {1,2}
f(1)=7-2(1)=5
f(2)=7-2(2)=3
Slope (m)=3/5
{7-2(1)}-{7-2(2)}=3-5=-2
In terms of n=-2n
The upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval is [5, 3]
Given the function of the graph bounded by the inteval [1, 2] expressed as
f(x) = 7 - 2x
The upper limit of the function is the point where the domain of the function x is 2. Substitute x = 2 into the function, we will have:
f(2) = 7 - 2(2)
f(2) = 7 - 4
f(2) = 3
For the lower limit, the domain of the function is at x = 2:
f(1) = 7 - 2(1)
f(1) = 7 - 2
f(1) = 5
Hence the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval is [5, 3].
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A manufacturing company measures the weight of boxes before shipping them to the customers. Assume that the weights of boxes are normally distributed with mean 90 lbs and standard deviation 24 lbs. a) Find the probability that a randomly selected box will exceed 94 lbs. b) If a sample of 36 boxes is randomly selected, find the probability that the average of the boxes exceeds 94 lbs.
Answer:
24
Step-by-step explanation:
In a large city, the city supervisor wants to find the average number of aluminum cans that each family recycles per month. So, she surveys 18 families and finds that these 18 families recycle an average of 140 cans per month with a standard deviation of 26 cans per month. Find the 90 % confidence interval for the mean number of cans that all of the families in the city recycle per month.
Answer:
The 90% onfidence interval for the mean number of cans that all of the families in the city recycle per month is between 129.34 and 150.66 cans per month
Step-by-step explanation:
We have the standard deviation of the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 18 - 1 = 17
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.74
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.74\frac{26}{\sqrt{18}} = 10.66[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 140 - 10.66 = 129.34 cans per month
The upper end of the interval is the sample mean added to M. So it is 140 + 10.66 = 150.66 cans per month.
The 90% onfidence interval for the mean number of cans that all of the families in the city recycle per month is between 129.34 and 150.66 cans per month
ratio 300 ml to 6 l
Answer:
20
Step-by-step explanation:
fist you convert 6l to ml=6×1000
then,300/300:6000/300
gives you 1:20
I'm having a hard time with this. A new housing development extends 4 miles in one direction, makes a right turn, and then con- tinues for 3 miles. A new road runs between the beginning and ending points of the development. What is the perimeter of the triangle formed by the homes and the road? What is the area of the housing development?
Answer:
perimeter = 12 miles
area = 6 square miles
Step-by-step explanation:
Since it makes a right triangle, use the Pythagorean Formula.
3^2+4^2=c^2
9+16=c^2
25=c^2
5=c, so the hypotenuse of the right triangle is 5.
Perimeter = 3+4+5 = 12 miles
area = 1/2bh (1/2 base times height)
=1/2x3x4
=6
Area = 6 square miles
The length of a rectangular garden is 3 yards greater
than the width of the garden. If the garden measures
15 yards diagonally, what is its length?
Answer:
12
Step-by-step explanation:
Let's call the width x and the length x + 3. Using the Pythagorean Theorem we can write:
(x + 3)² + x² = 15²
x² + 6x + 9 + x² = 225
2x² + 6x - 216 = 0
2(x² + 3x - 108) = 0
2(x + 12)(x - 9) = 0
x + 12 = 0 or x - 9 = 0
x = -12 or x = 9
x cannot be -12 because length/width can't be negative so x = 9 which means that the length is 9 + 3 = 12.