Answer:
378
Step-by-step explanation:
Work 1:She has 9 kinds of cards out of which she has to chose only 1.
The number of ways of doing this is 9 (she can pick any one of them).
Work 2:She has 7 kinds of cards out of which she has to chose only 1.
The number of ways of doing this is 7 (she can pick any one of them).
Work 3:She has 3 designs of first-class stamps out of which she has to chose only 1.
The number of ways of doing this is 3 (she can pick any one of them).
Work 4:She has to pick the color of pen and she has 2 to choose from.
The number of ways of doing this is 2 (she can choose any one of them).
She has to do Work 1 and Work 2 and Work 3 and Work 4.
∴By the fundamental counting principle, the total number of different ways in which the thank-you note can look is 9×7×3×2 = 378
what are the constant of proportionality for these two tables
A movie theater has n rows and m seats in each row. If each ticket costs $5.60, how much do all tickets to one movie cost?
Total cost of tickets for one movie showing is calculated by multiplying the total number of seats (n rows times m seats per row) by the cost per ticket, which is $5.60.
Explanation:To calculate the total cost of all tickets for one movie showing in a theater with n rows and m seats per row, you'll need to use multiplication to find the total number of seats and then multiply it by the cost per ticket. Here is a step-by-step guide:
Multiply the number of rows (n) by the number of seats per row (m) to find the total number of seats. This is n × m.Multiply the total number of seats by the cost per ticket, which is $5.60, to find the total cost for all tickets. This is (n × m) × $5.60.The final calculation will give you the total cost of tickets for one movie showing.For example, if a theater has 10 rows with 20 seats in each row, the total number of seats is 10 × 20 = 200. The total cost for all tickets would then be 200 × $5.60 = $1120.
Two points are located at (−9,−8) and (−6,−4).
Complete the equations below to show how you can use the Pythagorean theorem to find the distance between these two points.
Answer:
[tex]l(AB)=5\ units[/tex]
is the distance between the point A and point B.
Step-by-step explanation:
Let
A ≡ (x₁, y₁) ≡ (-9 , -8 )
B ≡ (x₂, y₂) ≡ (-6 , -4 )
Now by Pythagoras Distance formula we have
a² + b² = c²
[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}\\\\l(AB) = \sqrt{((-6--9)^{2}+(-4--8)^{2} )}\\\\l(AB)=\sqrt{(3)^{2}+(4)^{2} }\\\\l(AB) =\sqrt{25} \\\\l(AB) = 5\ units[/tex]
Answer
c= √(a² + b²)
c=√( -6 – -9 )² + ( -4 – -8 )²
Step-by-step explanation:
The first day of Alex's trip was a Monday. What was the day of the week on Alex's 39 day of his trip?
Answer: monday
Step-by-step explanation:
Using prime factorization what is the GCF 3y 2 squared, 24y 3 cubed
Answer:
[tex]3y^2[/tex]
Step-by-step explanation:
Given:
To find the GCF of [tex]3y^2\ and\ 24y^3[/tex] using prime factorization.
Writing each in prime factors:
3 = 1 [tex]\times[/tex] 3
24 = 1 [tex]\times[/tex] 2 [tex]\times[/tex] 2 [tex]\times[/tex]2 [tex]\times[/tex] 3
Now, GCF of 3 and 24 is 3
[tex]y^2=1\times y\times y[/tex]
[tex]y^3=1\times y\times y\times y[/tex]
GCF of [tex]y^2[/tex] and [tex]y^3[/tex] is [tex]y\times y=y^2[/tex].
Therefore, the overall GCF of the two terms is [tex]3y^2[/tex]
1) Which linear equation BEST represents the line of best fit for the scatterplot? A) y = x B) y = 3x C) y = -3x D) y = 5x + 1 2) Which graph shows no correlation? A) A B) B C) C D) D * Hover over answer image to enlarge 3) Which of the choices is the best example of a line of best fit for the scatterplot? A) A B) B C) C D) D * Hover over answer image to enlarge 4) The graph represents the current stock market trends. The best fit line shows A) no correlation B) weak positive correlation C) weak negative correlation D) strong positive correlation 5) Describe the correlation. A) no correlation B) prime correlation C) positive correlation D) negative correlation A survey was taken asking participants their age and how many soft drinks they drink a week. The results are displayed in the scatterplot. The data for people age 15-19 are not shown. Based on the scatterplot, how many soft drinks would 15-19 year olds be expected to drink in a week? A) 4 B) 6 C) 8 D) 14 7) Person BMI Total Cholesterol 1 20 157.87 2 22 170.85 3 24 183.83 4 26 196.81 5 28 209.79 6 30 222.77 7 32 235.75 Total Cholesterol and BMI were measured several individuals. Using the regression line, what is the expected total cholesterol if a person has a BMI of 35? A) 249.45 B) 253.21 C) 255.22 D) 257.43 8) The Dudley family just brought home twins from the hospital. Their neighbor's baby was born on the same day as the twins. A reasonable conclusion is that the Dudley family will spend more money on diapers. Is this association positive, negative, or neither? Is the relationship more likely a causation or correlation? A) neither B) positive; causation C) negative; correlation D) positive; correlation 9) Which causal relationship is justifiable? A) Children with bigger feet spell better. Spelling better causes a child's feet to grow. B) Surf board sales rise when lemonade sales rise. Drinking lemonade causes more people to buy surfing boards. C) The traffic is heavier around the stadium when a game is being played. Games being played cause more traffic. D) An elementary school child has more cavities than his baby brother. He also has a larger vocabulary. An increased vocabulary causes cavities. 10) Based on this graph, which statement MUST be true? A) More x causes less y. B) More x causes more y. C) There is a negative correlation between x and y. D) There is a positive correlation between x and y.
The questions pertain to the analysis of linear relationships between variables using scatter plots, lines of best fit through linear regression, and understanding correlation coefficients to identify the strength and direction of relationships in data.
Explanation:The questions provided are centered around the concepts of linear equations, scatter plots, correlation, and regression analysis in the realm of mathematics. Scatter plots are graphical representations showing the relationship between two variables. In these types of questions, the independent variable is plotted on the x-axis, and the dependent variable is plotted on the y-axis. To analyze the relationship, one can use linear regression to find the line of best fit, which is a straight line that best represents the data on a scatter plot. The correlation coefficient, often denoted as r, indicates the strength and direction of the linear relationship between two variables.
The line of best fit can be found by calculating the least-squares line, which minimizes the sum of the squares of the vertical distances of the points from the line. The equation of this line is typically in the form y = a + bx, where 'a' is the y-intercept and 'b' is the slope. The slope indicates how much the dependent variable changes for a one-unit change in the independent variable. The y-intercept is the value of the dependent variable when the independent variable is zero. A correlation coefficient of zero implies no linear relationship between the variables.
When looking at data such as stock market trends or health-related measurements like BMI and cholesterol, understanding the strength and type of correlation is essential for making predictions. For example, a positive correlation indicates that as one variable increases, the other variable tends to increase, while a negative correlation indicates the opposite. It's important to note that correlation does not imply causation; just because two variables are correlated does not mean that one causes the other.
Which of the following equations has an infinite number of
solutions?
3(2x+1)=2(1+3x)+1
3(2x+1)=2(1+3x)-1
3(2x-1)=2(1+3x)-1
3(2x+1)=2(3+2x)-3
The following equation has infinite many solutions
3(2x+1)=2(1+3x)+1
Step-by-step explanation:
An equation has infinite solutions if there is same constant on both sides of the equation.
We will check each equation one by one to find the equation with infinite solutions.
So,
3(2x+1)=2(1+3x)+1
[tex]3(2x+1)=2(1+3x)+1\\6x+3 = 2+6x+1\\6x +3 = 6x +3\\6x-6x+3 = 3\\3 = 3[/tex]
3(2x+1)=2(1+3x)-1
[tex]3(2x+1)=2(1+3x)-1\\6x+3 = 2+6x-1\\6x+3=1+6x\\6x-6x+3 = 1\\3 = 1[/tex]
3(2x-1)=2(1+3x)-1
[tex]3(2x-1)=2(1+3x)-1\\6x-3 = 2+6x-1\\6x-3 = 1+6x\\6x-6x-3 = 1\\-3 = 1[/tex]
3(2x+1)=2(3+2x)-3
[tex]3(2x+1)=2(3+2x)-3\\6x+3 = 6+4x-3\\6x+3 = 3+4x\\6x-4x+3 = 3\\2x+3 = 3[/tex]
The following equation has infinite many solutions
3(2x+1)=2(1+3x)+1
Keywords: Solution of equation, Linear equation
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Need some to answer this
500=(2xL)+(____x____)
500=2L+_______
_____=2L
_____ divided by 2=L
_____=L
A rectangular garden has a width of 90 feet. Thee predetermining of the garden is 500 feet what is the length of the garden
Answer:
The missing part is given below.
500=(2xL)+(__2__x_90___)
500=2L+__180_____
_320__=2L
_320____ divided by 2=L
_160____=L
Step-by-step explanation:
Given:
Perimeter of Rectangle = 500 feet
Width = 90 feet
Length = L
Solution:
[tex]\textrm{Perimeter of Rectangle} = 2(Length + Width)\\\\\textrm{On substituting the given values in it we get}\\500 = 2\times L + 2\times 90\\\\500 - 180 =2\times L\\320 =2\times L\\\\\frac{320}{2}=L\ ....................... (\textrm{320 divided by 2}) \\160 = L[/tex]
Final answer:
To find the length of the garden, the formula for the perimeter of a rectangle is used (P = 2L + 2W), where the perimeter is 500 feet and the width is 90 feet. By substituting these values and solving for L, we find that the length of the garden is 160 feet.
Explanation:
Finding the Length of a Garden
To find the length of a rectangular garden when you know the perimeter and the width, you can use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P stands for the perimeter, L is the length, and W is the width. The student has provided that the width (W) of the garden is 90 feet and the perimeter (P) is 500 feet.
Substituting the values we know into the formula, we get:
500 = 2L + 2(90)
Now, we solve for the length (L) by following these steps:
First, do the multiplication: 500 = 2L + 180
Next, subtract 180 from both sides to isolate the term with L: 320 = 2L
Finally, divide both sides by 2 to solve for L: 160 = L
Therefore, the length of the garden is 160 feet.
x-5y =30 and 10y=2x+90
Answer:
1. For x is x=5y+30 and for y is y=1/5x−6
2. For x is x=5y−45 and for y is y=1/5x+9
Step-by-step explanation:
A theater is selling tickets for a performance. Mr. Smith purchased 8 senior tickets and 5 child tickets for $136 for his friends and family. Mr. Jackson purchased 4 senior tickets and 6 child tickets for $96. What is the price of a senior ticket?
Answer:
The price of a senior ticket is $12.
Step-by-step explanation:
Given:
Mr. Smith purchased 8 senior tickets and 5 child tickets for $136. Mr. Jackson purchased 4 senior tickets and 6 child tickets for $96.
Now, to get what is the price of a senior ticket.
Let the senior ticket be [tex]x[/tex] and the child ticket be [tex]y[/tex]:
So, according to question
[tex]8x+5y=136[/tex].........(1)
[tex]4x+6y=96[/tex]...........(2)
Now, we have system of equations:
Multiplying the equation (2) by -2 we get:
[tex]-8x-12y=-192[/tex].......(3)
Now, adding the equation (3) and (1) the variables and the numbers:
[tex]-8x-12y+8x+5y=-192+136[/tex]
[tex]-7y=-56[/tex]
Dividing both sides by -7 we get:
[tex]y=8[/tex]
Putting the value of y in equation (2) we get:
[tex]4x+6(8)=96[/tex]
[tex]4x+48=96[/tex]
On solving the equation we get:
[tex]x=12[/tex].
Therefore, the price of a senior ticket is $12.
Choose all that are correct given the equation: y=1/4 x + 9
A.y=7.25 when x = -7
B.y=7 when x = -8
C.y=8.5 when x =-4
D.y=10.25 when x = 5
Answer: Option A, Option B, Option D.
Step-by-step explanation:
Let's check each option.
A. Substitute [tex]x=-7[/tex] into the equation and evaluate in order to find the value of "y". This is:
[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-7) + 9\\\\y=7.25[/tex]
B. Substitute [tex]x=-8[/tex] into the equation and evaluate in order to find the value of "y". Then:
[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-8) + 9\\\\y=7[/tex]
C. Substitute [tex]x=-4[/tex] into the equation and evaluate to find the value of "y":
[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-4) + 9\\\\y=8[/tex]
D. Substitute [tex]x=5[/tex] into the equation and then evaluate in order to find the value of "y". You get that this is:
[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(5) + 9\\\\y=10.25[/tex]
Then, the correct options are: Option A, Option B, Option D.
an = 5 × an-1 and a1 = 3.
What is a5
Enter your answer in the box.
A5 =
Answer:
[tex]A_{5} = 1875[/tex]
Step-by-step explanation:
The geometric sequence is represented by
[tex]A_{n} = 5 \times A_{n - 1}[/tex] .......... (1) and [tex]A_{1} = 3[/tex]
So, [tex]A_{2} = 5 \times A_{2 - 1} = 5 \times A_{1} = 5 \times 3 = 15[/tex]
{Putting n = 2}
Again, putting n = 3 in equation (1), we get
[tex]A_{3} = 5 \times A_{2} = 5 \times 15 = 75[/tex]
Again, putting n = 4 in equation (1), we get
[tex]A_{4} = 5 \times A_{3} = 5 \times 75 = 375[/tex]
Again, putting n = 5 in equation (1), we get
[tex]A_{5} = 5 \times A_{4} = 5 \times 375 = 1875[/tex] (Answer)
3.6792mm+2×10
[tex]36792mm + .2mm + .0133mm[/tex]
Answer:
36792.2133
Step-by-step explanation:
36792+0.2+0.0133=36792.2133
Find the first term and the common difference of the arithmetic sequence described. Give a recursive formula for the sequence. Find a formula for the n^th term
5th term is 0;
50 term is - 135
If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?
E
o y- 48 (2)
y (43)
O ya 4036
The expression will be y =8*2 or y = (48/6)*2
Step-by-step explanation:
The direct proportion is given if y varied directly as x
y∝x
When the proprtionality symbol is removed, a proportionality constant is introduced.
y = kx
as we know y = 48 when x = 6
[tex]48 = k * 6\\k = \frac{48}{6}\\k = 8[/tex]
The equation will be:
y = 8x
So when x=2
y = 8*2
y = 16
Hence,
The expression will be y =8*2 or y = (48/6)*2
Keywords: Proportion, Direct proportion
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To find the value of y when x is 2 in a direct variation, use the constant of variation k found from the given values (y = 48 when x = 6), which is 8 in this case, and multiply it by 2 to get y = 16.
If y varies directly as x, this means that y can be expressed as y = kx, where k is the constant of variation. Given that y = 48 when x = 6, we can find the value of k by substituting these values into the direct variation equation:
k = y/x = 48/6 = 8
Now that we have k, we can find the value of y when x is 2:
y = kx = 8 x 2 = 16
Therefore, the expression to find the value of y when x is 2 is y = 8 x 2.
Please help !!!!!!!!!!
Answer:
Yes (6,3) is a solution
Step-by-step explanation:
It because both of the lines that are shaded intercepted so it works for both
What is 80-5y when y=9
Answer:
Step-by-step explanation:
It’s 35 because 9*5 is 45 and 80-45 is 35
Please simplify the expression.
[tex]x^{7}[/tex] · [tex]y^{3}[/tex] · [tex]x^{8}[/tex] · [tex]y^{2}[/tex]
A. [tex]x^{15}[/tex] · [tex]y^{6}[/tex]
B. [tex]x^{15}[/tex] · [tex]y^{5}[/tex]
C. [tex]x^{56}[/tex] · [tex]y^{6}[/tex]
D. [tex]x^{56}[/tex] · [tex]y^{5}[/tex]
What is the equation to this graph????
Answer:
y=3x
Step-by-step explanation:
The slope of this graph is 3.
Write a division expression that is equivalent to 8/15 x (- 3/5)
Answer:
-8/15
Step-by-step explanation:
8*-3/15*5
=-24/75
= -8/15
Please it's urgent ans please
20) What is the closed linear form of the sequence 3,4,5,6,7, ...?
A) a= 2n
B) a = 2-n
C) a=3+n
a, = 3-n
The closed linear form of sequence 3, 4, 5, 6, 7, .. is a = 3 + n
Option C
Solution:
Given Sequence is 3, 4, 5, 6, 7, ...
Let us the check the each option which can form the above sequence
a) a= 2n
[tex]\begin{array}{l}{\text {For } n=0, a=2 \times(0)=0} \\\\ {\text {For } n=1, a=2 \times(1)=2} \\\\ {\text {For } n=2, a=2 \times(2)=4}\end{array}[/tex]
We get a sequence 0, 2, 4 which does not satisfy the given sequence
b) a= 2-n
[tex]\begin{array}{l}{\text {For } n=0, a=2-0=2} \\\\ {\text {For } n=1, a=2-1=1} \\\\ {\text {For } n=2, a=2-2=0}\end{array}[/tex]
We get a sequence 2, 1, 0 which does not satisfy the given sequence
c) a= 3+n
For n = 0, a = 3 + 0 = 3
For n = 1, a = 3 + 1 = 4
For n = 2, a = 3 + 2 = 5
For n = 3 , a = 3 + 3 = 6
For n = 4, a = 3 + 4 = 7
Which satisfy the given sequence
Hence, c) is the correct option
The closed linear form of the sequence 3, 4, 5, 6, 7, ... is a = 3 + n, which matches option C. The pattern in the sequence indicates that the nth term can be expressed as 3 + (n - 1). Therefore, the answer is option A: a = 2 + n.
To find the closed linear form, we identify the pattern in the sequence. The sequence starts at 3 and increments by 1 for each subsequent term. Hence, the nth term (an) can be expressed as:
an = 3 + (n - 1)
an = 2 + n
Therefore, the closed linear form of the given sequence is option A: a = 2 + n.
2.
Last week, the price of oranges at the farmer's market was $1.75 per pound. This
week, the price has decreased by 20%. What is the price of oranges this week?
Answer:
$1.40
Step-by-step explanation:
1.75-(1.75×.2)
1.75-.35
1.4
Answer:
$1.40
Step-by-step explanation:
100% - 20% = 80%
Therefore, Multiply $1.75 by 80% to get this week's price of orange
$1.75 x 80% = $1.40 per pound
Dustin always takes the same route when he walks his dog. First, he walks 6 blocks to the park. Then he walks 4 blocks to the elementary school. Finally, he walks 7 blocks to get back home. Dustin walks his dog 3 times each day. How many blocks does Dustin's dog walk each day?
Answer:
51
Step-by-step explanation:
add them altogether then times by 3
A point p in the first quadrant lies on the parabola y=x^2. Express the coordinates of p as a function of the angle of inclination of the line joining p to the origin
Answer:
The coordinates of the point p are: [tex](x,xtan\alpha )[/tex]
Explanation:
1. Name the angle of inclination of the line joining p to the origin α.
2. Find the relation between the coordinates of the point (x,y)
When you draw a line from the origin to the parabola, the intersection point, p(x,y) will have coordinates (x,y).
As per the definition of the tangent trigonometric ratio you have:
[tex]tan\alpha =\frac{y}{x}[/tex]From which you can clear y:
[tex]y=xtan\alpha =>(x,y)=(x,xtan\alpha )[/tex]Which is the expression of the coordinates of p as a function of the angle of inclination of the line joining p to the origin.
Jade normally leaves work at 5:00 pm, but she is leaving work 10 minutes late today. She decides to make up time by taking the toll road instead of side streets. She can travel two times faster by taking the toll road. Create an equation in terms of x to represent the number of minutes after 5:00 pm she arrives home from work if she leaves late. Let x represent the number of minutes her normal commute takes when she leaves on time.
y equals one half times x minus ten
y = 2x − 10
y = 2x + 10
y equals one half times x plus ten
Answer:
It will be answer choice D.
Step-by-step explanation:
It'll take the half the usual time because she is taking a road that get's her there 2 times faster, but also add 10 because she was 10 minutes late.
The linear equation in terms of x to represent the number of minutes after 5:00 pm she arrives home from work if she leaves late is (y = 0.5x + 10).
Given :
Jade normally leaves work at 5:00 pm, but she is leaving work 10 minutes late today. She decides to make up time by taking the toll road instead of side streets. She can travel two times faster by taking the toll road.Let x represent the number of minutes her normal commute takes when she leaves on time.According to the given, data x represent the number of minutes her normal commute takes when she leaves on time.
Let y be the total time taken by Jade after 5:00 pm to reach home. So, the linear equation that represents the given situation is:
[tex]\rm y = \dfrac{1}{2}x+10[/tex]
Therefore, the correct option is D).
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How much change does he need to receive back
Answer:
Damien will receive a change of [tex]\$4.69[/tex]
Step-by-step explanation:
Given:
Pair of jeans = $33
Sales tax = 7%
Money paid as Sales tax = 7% of sale done on pair of jeans = [tex]\frac{7}{100}\times \$33 = \$2.31[/tex]
Total amount paid = 40
We need to find the amount he will receive back
Amount receive back can be calculated by Total amount paid minus Amount for pair of jeans minus money paid as Sales Tax
Change amount received = Total amount paid - Amount for pair of jeans - money paid as Sales Tax = [tex]\$40 - \$33-\$2.31 = \$ 4.69[/tex]
Hence Damien will receive a change of [tex]\$4.69[/tex]
9. find the value of x ?
Answer:
B is the answer at least i think also are you in gaca? if so webmail me my name is Angela Petersen
Vivian has $57,366.66 in a savings account. The interest rate is 9 2/5%, compounded annually.
To the nearest cent, how much interest will she earn in 4 years
Answer:20652.00
Step-by-step explanation:
The formula would be p*r*t
p is the principal which is amount of money before interest
r is the interest rate
t is time period
so it would be 57,366.66*9 2/5%*4
9 2/5 as a decimal would be 9.4 or 0.09
57,366.66*9.4=539246.604*4=2156986.416
The correct amount would be $20652.00 in 4 years
Use 0.09 when u multiply instead of 9.4 because it is much easier
Factor the expression using the GCF.
14x + 63
Help! Please
The final factored expression using the GCF is: 14x+63=7(2x+9)
To factor the expression 14x + 63 using the Greatest Common Factor (GCF), let's first find the GCF of the numerical coefficients 14 and 63. The largest number that divides both 14 and 63 without a remainder is 7, making it the GCF.
Next, we divide each term by the GCF:
14x divided by 7 is 2x
63 divided by 7 is 9
Now that we have divided each term by the GCF, we can write the original expression as a product of the GCF and the simplified expression:
14x + 63 = 7(2x + 9)
This expression is fully factored as the product of the GCF (7) and the binomial (2x + 9).