Answer:
The answer would be the large album has 54 more stamps than the small album.
Step-by-step explanation:
... 92 - 38 = 54
Do you need a drawing done though?
The measurement of the height of 600 students of a college is normally distributed with a mean of
175 centimeters and a standard deviation of 5 centimeters.
What percent of students are between 170 centimeters and 180 centimeters in height?
16
34
68
81.5
Answer:
68
Step-by-step explanation:
We let the random variable X denote the height of students of the college. Therefore, X is normally distributed with a mean of 175 cm and a standard deviation of 5 centimeters.
We are required to determine the percent of students who are between 170 centimeters and 180 centimeters in height.
This can be expressed as;
P(170<X<180)
This can be evaluated in Stat-Crunch using the following steps;
In stat crunch, click Stat then Calculators and select Normal
In the pop-up window that appears click Between
Input the value of the mean as 175 and that of the standard deviation as 5
Then input the values 170 and 180
click compute
Stat-Crunch returns a probability of approximately 68%
Final answer:
Using the empirical rule for a normal distribution, approximately 68% of the students' heights fall within one standard deviation (170 cm to 180 cm) from the mean of 175 cm.
Explanation:
The student's question involves applying the empirical rule (also known as the 68-95-99.7 rule) for normally distributed data, which states that:
About 68% of the data falls within one standard deviation of the mean.
About 95% falls within two standard deviations.
About 99.7% falls within three standard deviations.
In this case, the mean height is 175 cm and the standard deviation is 5 cm. The student is interested in the percentage of students with heights between 170 cm and 180 cm, which corresponds to one standard deviation below and above the mean, respectively. Therefore, using the empirical rule, we can conclude that approximately 68 percent of the students' heights will lie in this range.
Find the area of the composite figure.
40 units2
38.5 units2
39.75 units2
44 units2
I Believe the Answer is 44 Units 2
Hope it helped, Not completely sure...
Answer:
The correct option is 4.
Step-by-step explanation:
It the given composite figure we have 3 triangles and 1 rectangle.
The area of a triangle is
[tex]A=\frac{1}{2}\times base\times height[/tex]
The area of first triangle is
[tex]A_1=\frac{1}{2}\times 4\times 3=6[/tex]
The area of second triangle is
[tex]A_2=\frac{1}{2}\times 4\times 3=6[/tex]
The area of third triangle is
[tex]A_3=\frac{1}{2}\times 8\times 2=8[/tex]
The area of a rectangle is
[tex]A=length \times width[/tex]
[tex]A_4=8 \times 3[/tex]
[tex]A_4=24[/tex]
The area of composite figure is
[tex]A=A_1+A_2+A_3+A_4[/tex]
[tex]A=6+6+8+24=44[/tex]
The area of composite figure is 44 units². Therefore the correct option is 4.
Which of these r-values represents the weakest correlation?
–0.9, –0.6, 0.2, 0.7
a. 0.2
b. -0.9
c. -0.6
d. 0.7
Answer:
0.2
Step-by-step explanation:
R can be as small as -1 to display a perfect negative linear relationship or as large as 1 to display a perfect positive linear relationship. The closer the r-value is to 0 the weaker the correlation so therefore 0.2 is closest to 0 making it the answer choice with the weakest correlation.
Jay J runs of a 1/3 mile in 4 minutes. A. If Jay J continues at the same speed, how long will it take her to run one mile?
[tex]\bf \begin{array}{ccll} miles&minutes\\ \cline{1-2} \frac{1}{3}&4\\\\ 1&x \end{array}\implies \cfrac{~~\frac{1}{3}~~}{1}=\cfrac{4}{x}\implies \cfrac{1}{3}=\cfrac{4}{x}\implies x=12[/tex]
Jim would like to create a pencil holder with no top. He would like it to be 5 inches taller and 3 inches wide. He can't decide if he would like to make it a square base or a circular base. If the material costs $0.75 per square inch, how much more would it cost him to make a square prism than a cylinder?
Answer:
[tex]\$11.13[/tex]
Step-by-step explanation:
step 1
Find the surface area of the cylinder
The surface area of the cylinder is equal to
[tex]SA=\pi r^{2} +2\pi rh[/tex]
we have
[tex]r=3/2=1.5\ in[/tex] ----> the radius is half the diameter
[tex]h=5\ in[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]SA=(3.14)(1.5)^{2} +2(3.14)(1.5)(5)=54.165\ in^{2}[/tex]
Find the cost
[tex]54.165*(0.75)=\$40.62[/tex]
step 2
Find the surface area of the square prism
The surface area of the prism is equal to
[tex]SA=b^{2} +4bh[/tex]
we have
[tex]b=3\ in[/tex]
[tex]h=5\ in[/tex]
substitute
[tex]SA=(3)^{2} +4(3)(5)=69\ in^{2}[/tex]
Find the cost
[tex]69*(0.75)=\$51.75[/tex]
step 3
Find the difference of costs
[tex]\$51.75-\$40.62=\$11.13[/tex]
(25pts) Due soon! Help!
Answer:
true
True
False
False
Step-by-step explanation:
a. The problem tells me that for every 3 parts of red paint, I have 8 parts of yellow paint. To find the ratio of 1 part of yellow paint I can write the following statement
For 8 parts of yellow paint ------------ 3 parts of red paint
1 part of yellow paint ------------- x
So [tex]x=\frac{1 part of yellow paint * 3 parts of red paint }{8 parts of yellow paint}[/tex]
[tex]x= \frac{3}{8} parts of red paint[/tex]
b, I have the following relationship
3 parts of red paint ----- 8 parts of yellow paint
If I multiply the entire expression by 3 I have left
3 * 3 parts of red paint -------- 8 * 3 parts of yellow paint
So
9 parts of red paint ---------- 24 parts of yellow paint
c.I have the same relationship
3 parts of red paint ----- 8 parts of yellow paint
If I multiply the entire expression by 1/2 I have left
3/2 parts of red paint -------- 8/2 parts of yellow paint
So
3/2 parts of red paint ---------- 4 parts of yellow paint
as 3/2 is different from 10, then the approach is false
d. observing the relation of part a,
For 3 parts of red paint ------------ 8 parts of yellow paint
1 part of red paint ------------- x
So [tex]x=\frac{1 part of red paint * 8 parts of yellow paint }{3 parts of red paint}[/tex]
[tex]x= \frac{8}{3} parts of yellow paint[/tex] that is different than 3/8 parts of yellow paint, then the approach is false
Answer:
true
True
False
False
Step-by-step explanation:
An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation 100e0.05t = 150 represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use your calculator and round to the nearest whole number.
Answer:
8
Step-by-step explanation:
edg
Answer:
8 years
Step-by-step explanation:
An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation [tex]100e^{0.05t} = 150[/tex] represents the situation, where t is the number of years the money has been invested.
To find out how long has the money invested we need to find out 't'
[tex]100e^{0.05t} = 150[/tex] , solve for t
divide both sides by 100
[tex]e^{0.05t} = 1.5[/tex]
Now to remove 'e' we take ln on both sides
[tex]ln(e^{0.05t) = ln 1.5[/tex]
the value of [tex]ln(e)= 1[/tex]
[tex]0.05t = ln 1.5[/tex]
Now divide by 0.05 on both sides
t = 8.10930
The money is invested for 8 years
The function f (x) has the value f (-1) = 1. The slope of the curve y = f (x) at any point is given by the expression dy/dx = (2x + 1)( y + 1)
1. Write an equation for the line tangent to the curve y = f (x) at x = ? 1.
2. Use the tangent line from part A to estimate f (?0.9)
3. Use separation of variables to find an explicit or implicit formula for y = f (x), with no integrals remaining.
4. What is the limit of f(x) as x approaches infinity?
1. When [tex]x=-1[/tex], you know that [tex]y=f(-1)=1[/tex]. The tangent line at [tex]x=-1[/tex] has slope
[tex]\dfrac{\mathrm dy}{\mathrm dx}(-1,1)=(2(-1)+1)(1+1)=-2[/tex]
Then the tangent line has equation
[tex]y-1=-2(x+1)\implies\boxed{y=-2x-1}[/tex]
2. Plug [tex]x=-0.9[/tex] into the equation for the tangent line to get
[tex]f(-0.9)\approx-2(-0.9)-1\implies\boxed{f(-0.9)\approx0.8}[/tex]
3. Separating the variables in the ODE gives
[tex]\dfrac{\mathrm dy}{y+1}=(2x+1)\,\mathrm dx[/tex]
Integrating both sides yields
[tex]\ln|y+1|=x^2+x+C[/tex]
Given that [tex]f(-1)=1[/tex], we get
[tex]\ln|1+1|=(-1)^2+(-1)+C\implies C=\ln2[/tex]
so that the particular solution to the ODE is
[tex]\ln|y+1|=x^2+x+\ln2\implies y+1=e^{x^2+x+\ln 2}\implies\boxed{y=2e^{x^2+x}-1}[/tex]
4. As [tex]x\to\infty[/tex], the exponential terms grows without bound, so that [tex]\boxed{f(x)\to\infty}[/tex] as well.
The length of a rectangle is 5 more than twice the width. Write an expression for the perimeter of a triangle.
A. 2x+5
B. 3x+5
C. 6x+10
D. 4x+10
Answer:
The correct answer is A.
Step-by-step explanation:
Because it is 5 more than, that would mean you would +5. And obviously twice meaning 2. So 2x+5 is the correct answer.
The correct Answer is A
identify the outlier in the data set of pledge amounts. then describe the effect the outlier has on the mean and median. $100, $17, $10, $20, $15, $32, $20, $40
The outlier is 100- it will raise the mean and shift the median
Final answer:
The outlier in the data set is $100, which substantially increases the mean, making it a less reliable measure of the central tendency than the median, which remains unaffected by the outlier.
Explanation:
To identify the outlier in the data set, we first arrange the pledge amounts in ascending order: $10, $15, $17, $20, $20, $32, $40, $100. The value $100 stands out as the outlier because it's significantly higher than the rest of the data.
The mean (or average) is calculated by adding all the numbers together and dividing by the total number of amounts, which is 8 in this case. The outlier can drastically increase the mean, making it less representative of the central tendency of the remaining data. The median, however, is the middle value of the ordered list. Since we have an even number of values, the median is the average of the two middle numbers. In the presence of an outlier, the median remains unaffected because it depends only on the middle values.
Therefore, the outlier has a greater effect on the mean than it does on the median, making the median a more reliable measure of central tendency in this scenario.
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $45,920. The variable costs will be $11.25 per book. The publisher will sell the finished product to bookstores at a price of $21.50 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
The publisher should produce and sell approximately 4480 books in order to break even on the total costs of production.
Explanation:The problem requires figuring out when the revenues from selling the book will equal the total cost of production. This is a problem in algebra.
The one-time fixed costs total $45,920, and the variable costs per book are $11.25. The books will be sold for $21.50 each.
Step 1: Set up an equation
Let x be the number of books that need to be sold. The equation is then: 45920 + 11.25x = 21.50x.
Step 2: Solve for x
Subtract 11.25x from each side to isolate the variable on one side giving you: 10.25x = 45920. Then, divide both sides by 10.25 to derive x. So, the equation is x = 45920 / 10.25.
Step 3: Derive the solution
By doing the calculation, x approximately equals 4480. Thus the publisher needs to sell just about 4480 books to break even.
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The publisher must produce and sell 4,478 books to cover total production costs. They need to break even by equating total costs with total revenue, using the formula FC + (VC × N) = P × N, and solving for N after substituting the given fixed costs, variable costs per book, and price per book.
Explanation:To determine how many books a publisher must produce and sell to cover production costs, the following formula is used:
Total costs (TC) = Fixed costs (FC) + (Variable cost per book (VC) × Number of books (N))Total revenue (TR) = Price per book (P) × Number of books (N)To break even, TC must equal TR. This can be expressed as:
FC + (VC × N) = P × N
Now we substitute the given values:
$45,920 + ($11.25 × N) = $21.50 × N
To find N, we solve the equation for N:
$45,920 = ($21.50 - $11.25) × NN = $45,920 / $10.25N = 4,478Therefore, the publisher must produce and sell 4,478 books to cover total production costs.
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Please help me out!!!!!!!!
Answer:
25[tex]\sqrt{x}[/tex]
Step-by-step explanation:
Using the rule of exponents
• [tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex], then
[tex]x^{\frac{1}{2} }[/tex] = [tex]\sqrt[2]{x^{1} }[/tex] = [tex]\sqrt{x}[/tex]
Hence
25 [tex]x^{\frac{1}{2} }[/tex] = 25[tex]\sqrt{x}[/tex]
If chord is 3 inches from the center and chord is 5 inches from the center of the same circle, then chord CD is the longer chord.
Step-by-step answer:
We know that for a given circle of radius R, the longest chord is the diameter, which is at 0 distance from the centre.
As we move the chord away from the centre, the chord length diminishes, up to at a distance R from the centre, the chord length is zero.
Therefore, the chord at 3 inches from the centre is longer than that at 5, assuming the radius is 5 inches or more.
Harold had 1,400 stamps. He gave 350 of them to his brother and the rest to his sister. What percent did he give to his brother?
Answer:
25%
Step-by-step explanation:
350/1400 as a simplified fraction is 1/4 because you can divide 350 into 1400.
And now we know that 1/4 is 25%.
Or just divide 1 by 4. And you'll get .25 and then just move the decimal to the right 2 times.
Hope this helps!
Harold gave 1,400 stamps to his brother and sister. He gave 350 stamps to his brother. What percent of stamps did Harold give to his brother.
The percent[tex]\frac{350}{1,400}[/tex] represents the number of stamps that Harold gave to his brother out of all the stamps.
To find what percent of stamps that Harold gave to his brother, we can change the fraction [tex]\frac{350}{1,400}[/tex] to a percent.
We can first reduce this fraction by dividing both the numerator and denominator by the Greatest Common Factor of 350 and 1400 using 350.
350 ÷ 350 = 1
1400 ÷ 350 = 4
Our reduced fraction is [tex]\frac{1}{4}[/tex].
1 ÷ 4 = 0.25
0.25 × 100 = 25%
Therefore, Harold gave his brother 25% of his stamps.
Find the cos of angle y
ANSWER
[tex]\cos(y) = \frac{4}{5} [/tex]
EXPLANATION
From the mnemonics SOH-CAH-TOA.
We want to find the cosine of y
CAH means cosine ratio involves adjacent over the hypotenuse.
[tex] \cos(y) = \frac{adjacent}{hypotenuse} [/tex]
From the right by triangle, the side ajacent to angle y is 64 units and the hypotenuse is 80 units.
[tex] \cos(y) = \frac{64}{80} [/tex]
[tex]\cos(y) = \frac{4}{5} [/tex]
Answer:4/5
Step-by-step explanation:
Find a whole number that, when added to the data set below, does not change the interquartile range. 80, 84, 86, 88, 88, 92, 94, 94
Answer:
An extra 95
Step-by-step explanation:
80 84 86 88 88 92 94 94
IQR = 9
80 84 86 88 88 92 94 94 94
IQR = 9
which polynomial is a trinomial? a.)1-x b.)1-2x+5x^4 c.)6-2x^3-4x^2+x^5 d.)2p^3-p
Answer: the answer is b
Step-by-step explanation:
Answer:
the answer is letter b.
[tex]1 - 2x + {5x}^{4} [/tex]
Pleaseeeeee help me!!
Answer:
118.3 m²
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 13 ( or 18.2) and h = 18.2( or 13) ← sides perpendicular
A = 0.5 × 13 × 18.2 = 118.3 m²
What is the midpoint of side AB in the triangle below?
A. ( -2 1/2, -1/2)
B. (1/2, 2 1/2)
C. (2 1/2, 1/2)
D. (-1/2, -2 1/2)
B
Step-by-step explanation:
half of 11 is 5.5 so counting that from either of the points leads to .5
Then continuing from there, half of 9 is 4.5 so moving the point up would get 2.5
Answer:
B
Step-by-step explanation:
How much pay does john receive if he gives half of his pay to family,250 to his landlord and has exactly 3/7 of his pay left over
Answer:
John receives a pay of $3,500.00
Step-by-step explanation:
x = John's pay
x = 1/2x + 250 + 3/7x [1/2 = 7/14 and 3/7 = 6/14]
x = 13/14x + 250
x - 13/14x = 13/14x - 13/14x + 250 [1x = 14/14]
1/14x = 250 [multiply both sides by 14]
x = 3500
Check:
3500 = 1/2(3500) + 250 + 3/7(3500)
3500 = 1750 + 250 + 1500
3500 = 3500
John's pay is -$3500. This means he owes money instead of receiving any pay.
Explanation:In order to calculate John's pay, we need to follow the given steps:
Step 1: Let's assume John's pay as 'x'.
Step 2: John gives half of his pay to his family. Therefore, he has (1/2)x left.
Step 3: John gives $250 to his landlord. Therefore, he has (1/2)x - $250 left.
Step 4: John has exactly 3/7 of his pay left over. Therefore, we can write the equation (1/2)x - $250 = (3/7)x and solve for 'x'.
To solve the equation, we can start by multiplying both sides by 14 to get rid of the denominators: 7((1/2)x - $250) = 14((3/7)x)
Simplifying both sides, we have 7x/2 - $250*7 = 6x
Combining like terms, we get 7x/2 - $1750 = 6x
Subtracting 7x/2 from both sides, we have -x/2 - $1750 = 0
Multiplying both sides by 2, we have -x - $3500 = 0
Adding $3500 to both sides, we have -x = $3500
Finally, multiplying both sides by -1, we have x = $-3500
Therefore, John's pay is -$3500. This means he owes money instead of receiving any pay.
The number of members of an online community increases each month. The function M(t) = N(1 + r)^t represents the number of members at month t, where N is the initial number of members and r is the rate of increase. Select the correct statement.
A. The value of M is a product of N and a factor that does not depend on N.
B. N increases each month.
C. The function is linear.
D. The initial value is (1 + r).
Answer:
A.
Step-by-step explanation:
On the right side of the equation we are multiplying the initial amount by the growth rate that is raised to a number of years. M is equal to this product. The growth rate does not depend upon the initial amount.
AT A STORE 3 SHIRTS AND 3 PANTS COST $93.75, AND 2 SHIRTS AND 4 PANTS COST $134.50 WHAT IS THE PRICE OF 1 SHIRT AND 1 PANT
Answer:
one shirt = $4.75 , one pant = $36
Step-by-step explanation:
Create two equations.
3p + 3s = 93.75
4p + 2s = 134.50
Use elimination by making s values the opposite of each other.
(3p + 3s = 93.75) -2
(4p + 2s = 134.50) 3
-6p -6s = -187.5
12p + 6s = 403.5
6p = 216
p = 36
Plug the cost of one pant into an equation
3(36) + 3s = 93.75
108 + 3s =93.75
14.25 = 3s
s = 4.75
I will set up the equations.
Let s = shirts
Let p = pants
3s + 3p = 93.75
2s + 4p = 134.50
Use the substitution method to find p and s.
Take it from here.
the three expressions, sin-1, cos-1, and tan-1 are called _____ trig functions and are used to find the measure of the acute angles of a right triangle if you know the lengths of at least two sides.
Answer:
Inverse.
Step-by-step explanation:
Answer:
theyre called inverse funtions .
inverse of :
cos= cosectant
tan= cotangent
sin= secant
Which triangle defined by three points on the coordinate plane is congruent with the triangle illustrated, and why?
A) (-1, 1)(-2, 1)(-1, 4); because corresponding pairs of angles are congruent.
B) (-2, -3)(-4, -3)(-2, -9); because corresponding pairs of angles are congruent.
C) (-1, 1)(-2, 1)(-1, 4); because corresponding pairs of sides and corresponding pairs of angles are congruent.
D) (-2, -3)(-4, -3)(-2, -9); because corresponding pairs of sides and corresponding pairs of angles are congruent
Answer:
D) (-2, -3)(-4, -3)(-2, -9); because corresponding pairs of sides and corresponding pairs of angles are congruent
Step-by-step explanation:
For triangles to be congruent, it is not enough that corresponding angles are congruent. In addition, there must be at least one pair of corresponding sides that are congruent. (Then all pairs will be congruent.)
The points listed in choices B and D are points that form a right triangle with leg lengths 2 and 6. However, choice B only refers to the angle measures, and not the sides. Choice D is the correct one.
To determine which triangle is congruent with the original triangle, we'll need specific criteria to compare. Congruent triangles have all corresponding sides and angles that are congruent, which means they will have the same size and shape but may be in different positions or orientations.
Assuming that the original (unillustrated) triangle has been given to us, we would compare it with the triangles listed in the options. However, without the original triangle's information, I can't directly compare it with the options given, so I will offer a step-by-step guide on how you could establish the congruence between triangles if the original triangle's dimensions were known.
Step 1: Determine the lengths of the sides of each of the given triangles using the distance formula, which is:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Step 2: Calculate the angles between each pair of sides using the dot product formula or by using the law of cosines. Remember that for angles, you might initially find the cosine of the angle with the dot product and then use the inverse cosine function to find the angle itself.
Step 3: Compare the lengths of sides and the measures of angles of the given triangles to those of the original triangle. If all sides and angles match, the triangles are congruent.
Step 4: Choose the correct answer based on which triangle has all three sides and angles that match the original triangle.
Let's briefly analyze the given triangles in the options:
Option A and Option C describe the same triangle: (-1, 1), (-2, 1), (-1, 4). In a congruence context, the reason for congruence would be the same whether it's because of corresponding pairs of angles or both sides and angles, but usually the congruence criteria involve both sides and angles (SSS, SAS, ASA, AAS).
Option B and Option D also describe the same triangle: (-2, -3), (-4, -3), (-2, -9). The reasoning provided once again does not fundamentally alter the congruence relationship since congruence should involve both sides and angles.
However, since we can't see the original triangle, I can't confirm which one is congruent. If you have the specific characteristics of the original triangle, you could use the steps outlined above to find out which triangle from these options is congruent with it. Remember, for two triangles to be congruent, they must have exactly the same three side lengths and the same three angles.
y = x ^ ( 2) - 6x + 2 rewrite in vertex form and state whether its maximum or minimum and give its coordinates
Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h,k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² - 6x
y = x² + 2(- 3)x + 9 - 9 + 2 = (x - 3)² - 7 ← in vertex form
with vertex = (3, - 7)
To determine whether maximum or minimum consider the value of a
• If a > 0 then minimum
• If a < 0 then maximum
here a = 1 > 0 ⇒ minimum
Hence (3, - 7) is a minimum
Ou have found a house that you would like to purchase. The amount of the home is $225,000. You would like to finance the home through your local credit union but they require a 10% down payment. Determine the amount needed for the down payment so that the bank will finance the home purchase. A. $22,500 c. $225,000 b. $202,500 d. $2,250
Answer:
A. $22,500
Step-by-step explanation:
10% = 10/100 = 1/10
To divide a decimal number by 10, move the decimal point one place to the left (remove a zero):
$225000./10 = $22500.0 = $22500
Find the inverse 2x+6/5
ANSWER
[tex]\frac{5x - 6}{2}[/tex]
EXPLANATION
The given function is
[tex] \frac{2x + 6}{5} [/tex]
Let
[tex]y = \frac{2x + 6}{5} [/tex]
Interchange x and y.
[tex]x= \frac{2y + 6}{5} [/tex]
Solve for y.
5x=2y+6
5x-6=2y
Divide both sides by 2
[tex] \frac{5x - 6}{2} = y[/tex]
Hence the given function has inverse
[tex]\frac{5x - 6}{2}[/tex]
The drama club sold 65 fewer adult tickets at $5 each than they did student tickets for $3 each. The total value of all the tickets was $675. How many adult and children tickets were sold?
Answer:
adults ticket sold= 60
student tickets =125
Step-by-step explanation:
So we need to make a system of equations. Lets say the variable a stands for adults tickets and the variable s stands for student tickets. Our first equation is going to be
s-a=65
that is because there are 65 more student tickets than adults.
the second equation is going to be
3s+5a=675
that is because the tickets will add up 675.
Now we have to make sure one of the variable cancels out when we add them together. So we have to multiply the first equation by 5.
5[s-a=65]
3s+5a=675
So then we end up with
5s-5a=325
3s-5a=675
We need to add them together and we end up with.
8s=1000
We need to divide by 8
s then equals 125.
So there are 125 students tickets.
We now plug 125 back into one of the equations. To make things easy lets to the first equation.
s-a=65
125-a=65
move the 125 over
-a=-60
multiply by a negative
a=60
So you have 60 adults tickets
Final answer:
By setting up and solving a system of equations, it's determined that 125 student tickets and 60 adult tickets were sold.
Explanation:
The task involves solving a system of equations to find out how many adult and student tickets were sold. Let the number of student tickets be s and the number of adult tickets be a. We have two pieces of information: First, the drama club sold 65 fewer adult tickets than student tickets, which translates to a = s - 65. Second, the total revenue from ticket sales was $675, with student tickets selling at $3 each and adult tickets at $5 each, giving us the equation 3s + 5a = 675.
To solve for s and a, we substitute the first equation into the second to get 3s + 5(s - 65) = 675. Simplifying this equation yields 8s - 325 = 675, so s = 125. Substituting s = 125 back into the first equation, a = 125 - 65, we find a = 60. Therefore, 125 student tickets and 60 adult tickets were sold.
A diver starts at the surface of the water and travels 8 feet to the bottom.
Graph A shows her distance from the bottom during the journey.
Graph B will show her distance from the surface during the journey.
Complete each statement about Graph B.
Answer:
On the graph B, at 0 seconds the graph will be at [tex]y=0.[/tex]
The graph will be going down until 2 seconds, when the diver reaches her deepest point. At 2 seconds the height of the graph will be -8ft.
Step-by-step explanation:
In graph B we are measuring the distance from the surface, that is we are setting the surface to be y=0. Thus if the diver reaches her deepest point 8ft down, she will be below y=0 and at -8ft.
Thus, in shape the graph B will be similar to graph A, but it will be shifted downed by 8ft.
Answer:
On Graph B, at 0 seconds, the graph will be at 0 feet.
Then the graph will increase until 2 seconds, when the diver reaches her deepest point. At 2 seconds the height of Graph B will be at 8 feet.
Step-by-step explanation:
It just works.
Given: p || q, and r || s.
Prove: ∠1 and ∠14 are supplementary angles.
What is the next step in the proof? Choose the most logical approach.
A.
Statement: ∠6 ≅ ∠14
Reason: For parallel lines cut by a transversal, corresponding angles are congruent.
B.
Statement: ∠6 ≅ ∠7
Reason: Vertical Angles Theorem
C.
Statement: ∠6 and ∠5 are supplementary.
Reason: Linear Pair Theorem
D.
Statement: m∠6 + m∠8 = 180°
Reason: angle addition
Answer:
A.
Statement: ∠6 ≅ ∠14
Reason: For parallel lines cut by a transversal, corresponding angles are congruent.
Step-by-step explanation:
In the figure attached, a plot of the problem is shown.
Given p || q and r is a transversal which cut p and q, then ∠1 ≅ ∠5 and ∠2 ≅ ∠6.
Given r || s and q is a transversal which cut r and s, then ∠6 ≅ ∠14 and ∠8 ≅ ∠16.
From the picture we see that ∠1 and ∠2 are supplementary, that is, their addition is equal to 180º. ∠2 ≅ ∠6 and ∠6 ≅ ∠14, then ∠2 ≅ ∠14, in consequence ∠1 and ∠14 are supplementary.
To prove that ∠1 and ∠14 are supplementary angles, given that p || q, and r || s, the next logical step in the proof is statement: ∠6 ≅ ∠14, with the reason being: for parallel lines cut by a transversal, corresponding angles are congruent.
Considering the given scenario: p is parallel to q and r is parallel to s, and the task is to prove that ∠1 and ∠14 are supplementary angles, the most logical step in this proof would be Option A.
Statement: ∠6 ≅ ∠14
Reason: For parallel lines cut by a transversal, corresponding angles are congruent.
This statement and reasoning holds true because when you have two parallel lines that are cut by a transversal, it produces corresponding angles that are congruent or equal in measure.
Hence, in the given scenario, since the lines p, q and r, s are parallel and are being cut by a transversal, it implies that ∠6 and ∠14 are equal in measure.
For more such questions on supplementary angles, click on:
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