Answer:
38 hot dogs114 sodasStep-by-step explanation:
Sometimes problems of this nature are easily worked by considering groups of items. Here, it is convenient to consider a group as 1 hot dog and 3 sodas, so the number of sodas in the group is 3 times the number of hotdogs in the group.
Each group is 4 items, so 152/4 = 38 groups were sold.
In the 38 groups, there were 38 hot dogs and 3×38 = 114 sodas.
114 sodas and 38 hot dogs were sold.
A garden measuring 12 meters by 6 meters is going to have a walkway constructed all around the perimeter, increasing the total area to 160 square meters. What will be the width of the pathway? (The pathway will be the same width around the entire garden).
Answer:
x=2
Step-by-step explanation:
Original width = 6
New width 6+x+x
Orignal length 12
New length 12+x+x
A = l*w
160 = ( 6+2x) ( 12+2x)
Factor
160 = 2( 3+x) 2(6+x)
Divide each side by 4
40 = (3+x) (6+x)
FOIL
40 = 18+ 6x+3x+ x^2
40 = 18 +9x+x^2
Subtract 40 from each side
0 = x^2 +9x -22
Factor
0 = (x +11) (x-2)
Using the zero product property
x +11 =0 x-2 =0
x= -11 x=2
Since we cannot have a negative sidewalk
x =2
Answer:
2
Step-by-step explanation:
Original width = 6
New width = 6 + x + x = 6 + 2x
Orignal length = 12
New length = 12 + x + x = 12 + 2x
A = l * w
160 = (6 + 2x)(12 + 2x)
160 = 2(3+x) * 2(6+x)
160 = 4 * (3 + x)(6 + x)
160/4 = (3 + x)(6 + x)
40 = 18 + 6x + 3x + x^2
40 = 18 + 9x + x^2
x^2 + 9x - 22 = 0
= x^2 + 11x - 2x - 22 = 0
= x(x + 11) - 2(x + 11) = 0
= (x + 11) (x - 2) = 0
x = - 11, 2
Since we cannot have a negative width because it's a dimension,
x = 2 is right
Share 32 beads between Joshua and kitty in the ratio 6:10 How much does Joshua gets ? Beads and kitty gets ?
Answer:one would get 12 one would get 20
Step-by-step explanation:just plug it in to the equation
Jodie Meeks's Free Throws During the 2015-16 NBA season, Jodie Meeks of the Detroit Pistons had a free throw shooting percentage of 0.906 . Assume that the probability Jodie Meeks makes any given free throw is fixed at 0.906 , and that free throws are independent.If Jodie Meeks shoots 6 free throws in a game, what is the probability that he makes at least 5 of them?
Answer:
0.8973
Step-by-step explanation:
Relevant data provided in the question as per the question below:
Free throw shooting percentage = 0.906
Free throws = 6
At least = 5
Based on the above information, the probability is
Let us assume the X signifies the number of free throws
So, Then X ≈ Bin (n = 6, p = 0.906)
[tex]P = (X = x) = $\sum\limits_{x}^6 (0.906)^x (1 - 0.906)^{6-x}, x = 0,1,2,3,.., 6[/tex]
Now
The Required probability = P(X ≥ 5) = P(X = 5) + P(X = 6)
[tex]= $\sum\limits_{5}^6 (0.906)^5 (1 - 0.906)^{6-5} + $\sum\limits_{6}^6 (0.906)^6 (1 - 0.906)^{6-6}[/tex]
= 0.8973
What is the value of log625^5 converted to a fraction
Answer:
1/4
Step-by-step explanation:
625^x = 5
x = 1/4
uppose that the length of 20 years worth of baseball games has been investigated, and that it has been found that the average (mean) length of a game is 165 minutes and the standard deviation is 30 minutes. What is the probability that a randomly selected game will last between 120 and 210 minutes
Answer:
P(120< x < 210) = 0.8664
Step-by-step explanation:
given data
time length = 20 year
average mean time μ = 165 min
standard deviation σ = 30 min
randomly selected game between = 120 and 210 minute
solution
so here probability between 120 and 210 will be
P(120< x < 210) = [tex]P(\frac{120-165}{30}< \frac{x-\mu }{\sigma } <\frac{210-165}{30})[/tex]
P(120< x < 210) = [tex]P(\frac{-45}{30}< \frac{x-\mu }{\sigma } <\frac{45}{30})[/tex]
P(120< x < 210) = P(-1.5< Z < 1.5)
P(120< x < 210) = P(Z< 1.5) - P(Z< -1.5)
now we will use here this function in excel function
=NORMSDIST(z)
=NORMSDIST(-1.5)
P(120< x < 210) = 0.9332 - 0.0668
P(120< x < 210) = 0.8664
The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 28 mm and standard deviation 7.6 mm.(a)What is the probability that defect length is at most 20 mm
Answer:
14.69% probability that defect length is at most 20 mm
Step-by-step explanation:
When the distribution is normal, we use 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.
In this question, we have that:
[tex]\mu = 28, \sigma = 7.6[/tex]
What is the probability that defect length is at most 20 mm
This is the pvalue of Z when X = 20. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20 - 28}{7.6}[/tex]
[tex]Z = -1.05[/tex]
[tex]Z = -1.05[/tex] has a pvalue of 0.1469
14.69% probability that defect length is at most 20 mm
A report about how American college students manage their finances includes data from a survey of college students. Each person in a representative sample of 793 college students was asked if they had one or more credit cards and if so, whether they paid their balance in full each month. There were 500 who paid in full each month. For this sample of 500 students, the sample mean credit card balance was reported to be $825. The sample standard deviation of the credit card balances for these 500 students was not reported, but for purposes of this exercise, suppose that it was $200. Is there convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than $905, the value reported for all college students with credit cards
Answer:
Yes. There is enough evidence to support the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.
Step-by-step explanation:
We want to test the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.
To perform this test we have a sample of 500 students which have paid their balance in full each month. The sample mean is $825 and the estimated sample deviation is considered $200.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=905\\\\H_a:\mu< 905[/tex]
The significance level is 0.05.
The sample has a size n=500.
The sample mean is M=825.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{200}{\sqrt{500}}=8.94[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{825-905}{8.94}=\dfrac{-80}{8.94}=-8.94[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=500-1=499[/tex]
This test is a left-tailed test, with 499 degrees of freedom and t=-8.94, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-8.94)=0[/tex]
As the P-value (0) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.
A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of eight cars form this company have an average gas mileage of 25.5 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported, assuming this is a normally distributed data set?
Answer:
[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]
The degrees of freedom are given by:
[tex]df=n-1=8-1=7[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]
Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense
Step-by-step explanation:
Information given
[tex]\bar X=25.5[/tex] represent the sample mean
[tex]s=1[/tex] represent the sample standard deviation
[tex]n=8[/tex] sample size
[tex]\mu_o =26[/tex] represent the value to verify
[tex]\alpha=0.06[/tex] represent the significance level
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Hypothesis to est
We want to test if the true mean is at least 26 mpg, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 25.5[/tex]
Alternative hypothesis:[tex]\mu < 25.5[/tex]
The statistic for this case is given by;
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]
The degrees of freedom are given by:
[tex]df=n-1=8-1=7[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]
Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense
At the kennel, the ratio of cats to dogs is 4:5. There are 27 animals in all. How many cats are in the kennel?
Answer:
Step-by-step explanation:
4x+5x=27
9x=27
x=27/9
x=3
4x3=12
5x3=15
The total number of cats were 12.
Based on the ratio of dogs to cats in the shelter, we know that out of 27 animals, there are 12 cats.
The ratio of cats to dogs is 4:5 which means that there are 5 dogs for every 4 cats.
This means that out of 9 animals, 4 would be cats and 5 would be dogs. If there was 27 animals therefore:
= 4 / 9 x 27
= 108 / 9
= 12 cats
In conclusion, there are 12 cats.
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A sinusoid is any function whose values repeat in a periodic manner.
A. True
B. False
SUBMIT
Answer: short answer
Just checked it’s False
Hope this helps :))
Step-by-step explanation:
Answer:
B. False
Step-by-step explanation:
A P E X
Given that (- 2, 7) is on the graph of f(x) , find the corresponding point for the function f(x + 4).
Answer:
[tex]\boxed{\ the \ corresponding\ point\ is \ (-6,7)\ }[/tex]
Step-by-step explanation:
We know that f(-2)=7
x+4 = -2 <=> x = -6
so f(-6+4) = f(-2)=7
then the corresponding point is (-6,7)
what is the least common denominator of 4 7/9 and 2 2/3
Answer:
9
Equivalent Fractions with the LCD
4 7/9 = 43/9
2 2/3 = 24/9
For the denominators (9, 3) the least common multiple (LCM) is 9.
Therefore, the least common denominator (LCD) is 9.
4 7/9 = 43/9 × 1/1 = 43/9
2 2/3 = 8/3 × 3/3 = 24/9
Hope this helps :)
The least common denominator of 4 7/9 and 2 2/3 is 9.
Given data:
To find the least common denominator (LCD) of 4 7/9 and 2 2/3, we need to first convert both fractions to their equivalent forms with a common denominator.
The given fractions are:
4 7/9 = 4 + 7/9
2 2/3 = 2 + 2/3
To find a common denominator, we need to find the least common multiple (LCM) of the denominators 9 and 3, which is 9.
Now, let's convert the fractions to their equivalent forms with a denominator of 9:
4 7/9 = (4 * 9)/9 + (7/9) = 36/9 + 7/9 = 43/9
2 2/3 = (2 * 9)/9 + (2/3) = 18/9 + 2/3 = 20/9
The fractions 4 7/9 and 2 2/3 are now expressed with a common denominator of 9.
Hence, the least common denominator (LCD) of 4 7/9 and 2 2/3 is 9.
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What is the image of (-4,12) after a dilation by a scale factor of 1/4 centered at the origin
Answer:
(-1,4)
Step-by-step explanation:
Divide each imput by 4
The required image of the given point (-4, 12) dilation by a scale factor of 1/4 and centered at the origin is (1, -3).
Given that,
To determine the image of (-4,12) after dilation by a scale factor of 1/4 centered at the origin.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph
Here,
For the point, we have a dilation factor of 1/4,
So dilated coordinate,
= (1/4 * - 4 , 1/4 * 12)
= (-1 , 3)
To form the image across the origin
= - (-1, 3)
= (1, -3)
Thus, the required image of the given point (-4, 12) with a scale factor of 1/4 and centered at the origin is (1, -3).
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Please answer this correctly
Answer:
3.14
Step-by-step explanation:
We find the total circumference of a circle with radius 2 to be
2 * pi * r
= 2 * 3.14 * 2
= 12.56
We divide by 4 to get the perimeter of the quarter circle
12.56/4 = 3.14
Solve: x - 1 < 3 help me plssss
Answer:
x =2
Step-by-step explanation:
becaue 2-1 is smaller than 3
Answer:
Hello!
I believe your answer is:
x=2
If this is not correct, please let me know and I will try again!
Step-by-step explanation:
Twice the length of the rectangle exceeds three times the width of the rectangle by one centimeter and if one-third of the difference of the length and the width is one centimeter.find the dimension.
The dimensions of the rectangle are given as 4cm and 1cm respectively.
What is a rectangle?A rectangle is a type of parallelogram having equal diagonals.
All the interior angles of a rectangle are equal to the right angle.
The diagonals of a rectangle do not bisect each other.
Suppose the length of rectangle be x.
And, the width be y.
Then, the following equations can be written as per the information given as,
2x - 3y = 1 (1)
And, 1/3(x - y) = 1
⇒ x - y = 3 (2)
Multiply equation (2) by 2 and subtract from (1) to get,
2x - 3y - 2(x - y) = 1 - 2 × 3
⇒ -5y = -5
⇒ y = 1
Substitute y = 1 in equation (2) to get,
x - 1 = 3
⇒ x = 4
Hence, the dimensions are 4cm and 1cm respectively.
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Which is required for sexual reproduction?
Answer:
2 parents are required
Step-by-step explanation:
Answer:
semen.............
−2.73(m+4)=−6m−4.38.
Answer:
m=2
Step-by-step explanation:
-2.73m-10.92=-6m-4.38
3.27m=6.54
m=2
Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $ 500 500, 3 prizes of $ 200 200, 5 prizes of $ 10 10, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket?
Answer:
-$0.75
Step-by-step explanation:
For calculation of expected value first we need to find out the probability distribution for this raffle which is shown below:-
Amount Probability
500 - 1 = $499 1 ÷ 5,000
200 - 1 = $199 3 ÷ 5,000
10 - 1 = $9 5 ÷ 5,000
5 - 1 = $4 20 ÷ 5,000
-$1 5,000 - 29 ÷ 5,000 = 4,971 ÷ 5,000
Now, the expected value of raffle will be
[tex]= \$499 \times (\frac{1}{5,000}) + \$199 \times (\frac{3}{5,000}) + \$9 \times (\frac{5}{5,000}) + \$4 \times (\frac{20}{5,000}) - \$1 \times (\frac{4,971}{5,000})[/tex]
= 0.0998 + 0.1194 + 0.009 + 0.016 - 0.9942
= -$0.75
The expected value of this raffle per ticket is $ 0.25.
Given that five thousand tickets are sold at $ 1 each for a charity raffle, and tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $ 500, 3 prizes of $ 200, 5 prizes of $ 10, and 20 prizes of $ 5, to determine what is the expected value of this raffle if you buy 1 ticket, the following calculation must be performed:
(500 + 3 x 200 + 5 x 10 + 20 x 5) / 5000 = X (500 + 600 + 50 + 100) / 5000 = X 1250/5000 = X 0.25 = X
Therefore, the expected value of this raffle per ticket is $ 0.25.
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Find the length of side x in simplest radical form with a rational denominator
Answer:
[tex] x = 7 \sqrt{3} [/tex]
Step-by-step explanation:
[tex] \tan \: 30 \degree = \frac{7}{x} \\ \\ \therefore \: \frac{1}{ \sqrt{3} } = \frac{7}{x} \\ \\ x = 7 \sqrt{3} \\ [/tex]
what is 2n+3n +1 +8n+4
Answer:
13n + 5
Step-by-step explanation:
2+3+8 = 13n
1+4 = 5
13n+5
What sit he shape of the cross section formed when’s. Cone intersects a plane as shown in the drawing?
Give me a reason why tok
Answer: Option D.
Step-by-step explanation:
Here we see the cross-section of a cone when it is cut by a plane that is parallel to the base of the cone.
As the plane is parallel to the base, we expect to see a figure that has the same shape as the base ( a circle) (you can think that over the plane we have a smaller cone, and the base of that cone also must be circular)
So the correct option is D.
Pamela is a college student. She pays tuition every semester and rent every month, and she uses cash daily for food. The expression 2x+12y+365z represents her yearly expenses. Which variable represents her rent?
Answer:
Variable y represent the rent of Pamela
Step-by-step explanation:
Given
Pamela pays tuition every semester and rent every month, and she uses cash daily for food.
lets understand what constitute semester , month and day in a year.
A semester consist of 6 months.
As a year has 12 months , a year will have 2 semester.
If one pays x for one semester then in a year one has to pay 2x .
As a year has two semester
Similarly
A year has 12 months .
If one pays y for one month then in a year one has to pay 12y .
As a A year has 12 months .
A year has 365 days
If one pays z for each month then in a year one has to pay 365z .
As a A year has 365 days.
__________________________________________
Based on above discussion , we can now safely assume that the we have to look at the coefficient of expression 2x+12y+365z to find the which variable represent which type of bill.
As we have to find variable for rent and rent is paid monthly.
so for a year total bill will have 12 months and hence going by expression variable y represent the rent of Pamela.
i need help in homework no guess
Answer:
No
Step-by-step explanation:
Use the vertical line test. If the line intercepts more than one point, it is not a function. Since there are two points where the value of 'x' is two, the line will pass both points. The graph is not a function.
1. In an arithmetic sequence, the first term is -2, the fourth term is 16, and the n-th term is 11,998
(a) Find the common difference d
(b) Find the value of n.
pls help...
Answer:
see explanation
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
(a)
Given a₁ = - 2 and a₄ = 16, then
a₁ + 3d = 16 , that is
- 2 + 3d = 16 ( add 2 to both sides )
3d = 18 ( divide both sides by 3 )
d = 6
--------------
(b)
Given
[tex]a_{n}[/tex] = 11998 , then
a₁ + (n - 1)d = 11998 , that is
- 2 + 6(n - 1) = 11998 ( add 2 to both sides )
6(n - 1) = 12000 ( divide both sides by 6 )
n - 1 = 2000 ( add 1 to both sides )
n = 2001
------------------
A marketing analyst randomly surveyed 150 adults from a certain city and asked which type of tooth paste they were currently using - Extra Whitening or Regular. 96 said they were currently using Extra Whitening while the rest said they were using Regular. The analyst wants to determine if this is evidence that more than half of the adults in this city are using Extra Whitening. Suppose a p-value from the correct hypothesis test was 0.0003. Which of the following is a correct interpretation of this p-value?
A. HA: p_extra White > p_Regular.
B. HA: p > 0.5, where p = the proportion of all adults in this city using Extra Whitening.
C. HA: p = 0.64, where p = the proportion of all adults in this city using Extra Whitening.
D. HA: p=0.5, where p = the proportion of all adults in this city using Extra Whitening.
Please answer this correctly
Answer:
20 total
Shelves 3 shelves /20 total=0.15=15%
Signs 2/20=0.10=10%
Benches 6/20=0.30=30%
Tablet Holders 9/20=0.45=45%
Step-by-step explanation:
Answer:
Shelves: 15%
Signs: 10%
Benches: 30%
Tablet Holders: 45%
Step-by-step explanation:
Shelves: [tex]\frac{3}{3+2+6+9} =\frac{3}{20} =\frac{15}{100} =[/tex] 15%
Signs: [tex]\frac{2}{3+2+6+9} =\frac{2}{20} =\frac{10}{100} =[/tex] 10%
Benches: [tex]\frac{6}{3+2+6+9} =\frac{6}{20} =\frac{30}{100}=[/tex] 30%
Tablet Holders: [tex]\frac{9}{3+2+6+9} =\frac{9}{20} =\frac{45}{100} =[/tex] 45%
In a group, 10 freshmen have mean GPA of 3.5; 20 sophomores have a mean GPA of 2.9; 25 juniors have a mean GPA of 3.2; and 15 seniors have a mean GPA of 3.4. What is the mean of the entire group
Answer:
[tex] T_1 = 10*3.5 = 35[/tex]
[tex] T_2 = 20*2.9 = 58[/tex]
[tex] T_3 = 25*3.2 = 80[/tex]
[tex] T_4 = 15*3.4 = 51[/tex]
[tex] \bar X= \frac{T_1 +T_2 +T_3 +T_4}{10+20+25+15}= \frac{35+58+80+51}{10+20+25+15} = 3.2[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] n_1= 10 , \bar X_1 = 3.5[/tex] for freshmen
[tex] n_2= 20 , \bar X_2 = 2.9[/tex] for sophomores
[tex] n_3= 25 , \bar X_3 = 3.2[/tex] for juniors
[tex] n_4= 15 , \bar X_4 = 3.4[/tex] for seniors
For this case we can use the formula for the sample mean in order to find the total of each group:
[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]T= \sum_{i=1}^n X_i = n *\bar X[/tex]
And replacing we got:
[tex] T_1 = 10*3.5 = 35[/tex]
[tex] T_2 = 20*2.9 = 58[/tex]
[tex] T_3 = 25*3.2 = 80[/tex]
[tex] T_4 = 15*3.4 = 51[/tex]
And the grand mean would be given by:
[tex] \bar X= \frac{T_1 +T_2 +T_3 +T_4}{10+20+25+15}= \frac{35+58+80+51}{10+20+25+15} = 3.2[/tex]
Evaluate x - 2y when x = 5 and y = 5.
Determine whether the ordered pair satisfies the equation.
x - 2y = -5; (5,5)
Yes, the ordered pair satisfies the equation.
No, the ordered pair does not satisfy the equation.
Answer:
For the first question we just plug in the values so we get 5 - 2 * 5 = -5.
Again, for the second one we'll plug in the values and see if it's a true statement. 5 - 2 * 5 = -5 and -5 = -5 so the answer is yes.
Which steps can be used to solve for the value of y?
(2013
(y +57) = 178
Answer: [tex]y = 121[/tex]
[tex](y+57) = 178[/tex]
[tex]y+57= 178[/tex]
[tex]y = 178 -57[/tex]
[tex]y = 121[/tex]
