During The Month Of October, Sophie Raised $25 for a charity. During November, she raised 5 times as much money for charity. How much money did sophie raise in November
The price of a cantaloupe at a fruit stand goes up 4 cents each month. The first month the stand was open, a cantaloupe cost $1.25.
What will the cost of a cantaloupe be in the 40th month?
A. $157.25
B. $16.85
C. $3.35
D. $2.81
Answer:
D. $2.81
Step-by-step explanation:
The statement says that the price of a cantaloupe goes up 4 cents each month and that the cost of the cantaloupe was $1.25 on the first month. Tto determine the cost in the 40th month, you have to multiply 4 cents for 39 months as the price for the first month was given and then you have to add this with the price for the first month:
0,04*39= 1.56
1.56+1.25= $2.81
The price in the 40th month is $2.81.
A rectangle has side lengths of a and b, which are non-zero integers. Determine possible values of a and b, which will make the diagonal of the rectangle a rational number.
A) a=1, b=1
B) a=4, b=5
C) a=3, b=4
D) a=1, b=2
Look at the picture.
Use the Pythagorean theorem:
[tex]a^2+b^2=d^2[/tex]
A) a = 1, b = 1
[tex]d^2=1^2+1^2\\\\d^2=1+1\\\\d^2=2\to d=\sqrt2\ \text{it's not rational number}[/tex]
B) a = 4, b = 5
[tex]d^2=4^2+5^2\\\\d^2=16+25\\\\d^2=41\to d=\sqrt{41}\ \text{it's not rational number}[/tex]
C) a = 3, b = 4
[tex]d^2=3^2+4^2\\\\d^2=9+16\\\\d^2=25\to d=\sqrt{25}\to d=5\ \boxed{:)}[/tex]
D) a = 1, b = 2
[tex]d^2=1^2+2^2\\\\d^2=1+4\\\\d^2=5\to d=\sqrt5\ \text{it's not rational number}}[/tex]
Answer: C) a = 3, b = 4.Options A, B, and D do not yield a perfect square, while option C does, with a=3 and b=4 resulting in a rational diagonal length of 5.
The diagonal of a rectangle can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, this is represented as [tex]c^2 = a^2 + b^2,[/tex] where a and b are the sides of the rectangle and c is the diagonal.
Looking at the given options:
A) a=1, b=1: Here, [tex]a^2 + b^2 = 1^2 + 1^2 = 2,[/tex] it is not a perfect square, so the diagonal will not be rational.B) a=4, b=5: Here, [tex]a^2 + b^2 = 4^2 + 5^2 = 16 + 25 = 41,[/tex] it is not a perfect square, so the diagonal will not be rational.C) a=3, b=4: Here, [tex]a^2 + b^2 = 3^2 + 4^2 = 9 + 16 = 25[/tex], it is a perfect square (5^2), so the diagonal is rational.D) a=1, b=2: Here, [tex]a^2 + b^2 = 1^2 + 2^2 = 1 + 4 = 5,[/tex] it is not a perfect square, so the diagonal will not be rational.Therefore, the possible values of a and b which will make the diagonal of the rectangle a rational number are given in option C: a=3 and b=4.
A student multiplied –8 × 334 as shown. One step is missing. Which is the missing step? –8 × 334 = ? = –8 × 3 + (–8) × 34 = –24 + −8 × 324 = –24 + −244 = –24 + (–6) = –30
Answer:
–24 + −8 × 324
Step-by-step explanation:
Well, if you go through the answer choices, there is only one that gives you the correct answer. The product is -2672, and the only answer choice that this satisfies is the second one.
Answer:
It's C
Step-by-step explanation:
Which best describes this triangle?
A.
All sides are the same length; each angle measures 90°.
B.
Two sides are the same length; one angle measures 90°.
C.
Two sides are the same length; one angle is obtuse.
D.
All sides are the same length; each angle is acute.
Mrs. Johnson is 3 times as old as her son. Ten years ago she was 5 times as old as her son was then. Find each of their ages
Answer:
her son is 20, Mrs. Johnson is 60
Step-by-step explanation:
if her son is x, Mrs. Johnson is 3x,
Ten years ago,
her son is x-10, Mrs. Johnson is 3x-10,
so:
3x-10=5(x-10)
x=20
Which angles are corresponding angles
Answer:
Step-by-step explanation:
corresponding angles are congruent to eachother for example 1&3, 5&7, 2&4, 8&6
Answer:
Option B, C, D are the correct options
Step-by-step explanation:
When two parallel lines are intersected by a transverse then two angle which are relatively at the the same position are called as corresponding angles.
As given in the picture attached, ∠1 and ∠2 are corresponding angles.
Similarly, ∠3 and ∠4 re corresponding angles.
Now we come to our question. In this question corresponding angles are
1) 2 and 4
2) 6 and 8
3) 1 and 3
4) 5 and 7
Therefore, Options. B, C and D are the correct options.
Simplify the expression
Answer:
729
Step-by-step explanation:
[(-1)^3]^2 /[(-3)^-3]^2
= 1 * [(-3)^3]^2
= 1 * 729
= 729
Answer:
729
To solve this, we need to start on the inside and work out; solving one part at a time.
[{(-1)^3 / (-3)^-3}]^2
1. (-1)^3 = -1
2. (-3)^-3 = - 1/27
3. (-1) / (- 1/27) = 27
4. 27^2 = 729
Each year the soccer team, Peterson United, plays 25 games at their stadium. The owner of Peterson United claimed that last year the mean attendance per game at their home stadium was 24500.
Based on the owner´s claim, calculate the total attendance for the game at Peterson United´s home stadium last year.
High school question
3 parts
Answer:
Total attendance for the game at stadium last year was 612500.
Step-by-step explanation:
Each year the soccer team, Peterson United, plays 25 games at their stadium.
The owner of Peterson United claimed that last year the mean attendance per game was = 24500
Since mean of any set of data = [tex]\frac{sum of data}{Total number of data}[/tex]
When we apply this rule in this question formula becomes as
24500 = [tex]\frac{x}{25}[/tex]
x = 25 × 24500
x = 612500
100 points!
Only 29 and 31
Rewrite each expression eliminating fractions. Simplified answers may be left in terms of any of the six trigonometric functions.
Answer:
29. sec w csc w - sec^2 w
31. - tan ^2 k (sin k +1)
Step-by-step explanation:
29. (cot w -1)/ (1- sin^2 w)
We know that cot w = cos w/ sin w
and 1 - sin^2 w = cos ^2 w
Replace these identities into the expression
(cos w/ sin w -1)
-----------------------
cos ^ 2 w
Get a common denominator on top of sin w
(cos w/ sin w -sin w/sin w)
-----------------------
cos ^ 2 w
(cos w - sinw)/ sin w
-----------------------
cos ^ 2 w
(cos w - sinw)
-----------------------
cos ^ 2 w sin w
Split into 2 terms
cos w sin w
----------------------- - ---------------------------------
cos ^ 2 w sin w cos ^2 w sin w
Cancel cos w in the first term and sin w in the second term
1 1
----------------------- - ---------------------------------
cos w sin w cos ^2 w
We know that 1/cos = sec and 1/ sin = csc
sec w csc w - sec^2 w
31. sin k/ (1 - csc k)
We know that csc k is 1/ sin k
sin k
---------------
1 - 1/ sin k
Get a common denominator for the bottom
sin k
---------------
sin k/ sin k - 1/ sin k
sin k
---------------
(sin k-1)/ sin k
Multiply by sin k/sin k
sin k * sin k
---------------
(sin k-1)/ sin k * sin k
sin k * sin k
---------------
(sin k-1)
sin^2 k
---------------
(sin k-1)
Multiply by (sin k +1)/ (sin k +1) so we can get rid of the denominator
sin^2 k (sin k +1)
-------------------------
(sin k-1) (sin k +1)
Foiling out the denominator, we get (sin^2 k-1)
sin^2 k (sin k +1)
-------------------------
(sin^2 k-1)
Factoring out a -1 from the denominator
sin^2 k (sin k +1)
-------------------------
-1 (1 - sin^2 k)
1 - sin ^2 k = cos ^ k
sin^2 k (sin k +1)
-------------------------
-1 (cos ^2 k)
sin ^2k/ cos ^2 k = tan ^2 k
- tan ^2 k (sin k +1)
How many 3 over 8 pound bags of trail mix can be made from 6 and 3 over 8 pounds of trail mix ? Write a division expression
Answer:
[tex]\frac{\frac{51}{8}} {\frac{3}{8}}[/tex]
17 bags.
Step-by-step explanation:
We are asked to find the number of bags with weight 3/8 pound can be made from [tex]6\frac{3}{8}[/tex].
To find the number of
[tex]\text{Number of bags that can be made from available mix trail}=6\frac{3}{8}\div \frac{3}{8}[/tex]
Convert mixed fraction into improper fraction.
[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{8}\div \frac{3}{8}[/tex]
Since we know that dividing a fraction with another fraction is same as multiplying the 1st fraction with the reciprocal of 2nd fraction.
[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{8}\times \frac{8}{3}[/tex]
After cancelling out 8 from numerator and denominator we will get,
[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{3}[/tex]
[tex]\text{Number of bags that can be made from available mix trail}=17[/tex]
Therefore, 17 bags each of weight 3/8 pounds can be made from [tex]6\frac{3}{8}[/tex] pounds of mix trail.
Marco books a room at a hotel. He spends $600 in total for a 3-night stay. Fill in each statement. For every 1 night that Marco stays at the hotel, he spends . If he stays at the hotel for 5 nights, he would spend .
Line segment AB has a length of 15 and angle a=35degrees . A segment with a length of 12 will form the third side of the triangle. What are the possible measures of the angle opposite side AB? Please explain the process.
Answer:
C = 45.8 or C = 117.69
Step-by-step explanation:
Remark
Only SSA gives the possibility of 2 answers. This one does not give that opportunity. There is one unique answer. We'll discuss 2 and zero after finding 1 answer. On looking at it again, the question might be ambiguous. We'll check that out as well.
Given
AB = 15
<A = 35
point C opposite line AB such that CB = 12 These givens give a unique answer.
Solution
Sin(35) / 12 = Sin(C) / 15 Multiply both sides by 15
15*Sin(35) / 12 = Sin(C) Find 15/12
1.25*sin(35) = Sin(C) Write Sin(35)
1.25*0.5736 = Sin(C) Multiply the left
0.71697 = Sin(C) Take the inverse Sin
C = 45.805 degrees This is the angle opposite AB
Angle B = 180 - 35 - 45.805 = 99.2
Ambiguous Case
If AC = 12 we have another answer entirely. This is SAS which will give just 1 set of answers for the triangle. The reason the case is ambiguous is because we don't exactly know where that 12 unit line is. It could be AC or BC.
I will set up the Sin law for you, and let you solve it
Sin(B) / 12 = Sin(35)/15
When you solve for Sin(B) as done above you, get 0.45886 from which B = 27.31 degrees
C = 180 - 35 - 27.31 = 117.69
So that's two values that C could have. I think that's all given these conditions.
Two Cases or None
<A = 35 degrees
AC = 15
CB = 12
This should give you two possible cases or none. You can check which by finding the height of the triangle from C down to AB (which has no distinct length. The h is 15 * Sin35 = 8.6. If CB < 8.6, there are no solutions. If CB < AC then if CB > that 8.6, there are 2 solutions.
Find the domain of the following graph:
−7 < x ≤9
−7 < y ≤ 9
−7 < x ≤5
−7 < y ≤ 5
Answer:
[tex]-7<x\leq 9[/tex]
Step-by-step explanation:
The domain is the set of all x-values. We can find the domain by finding the left boundary of the graph (the furthest left x-value) and then the right boundary (the furthest right x value).
The furthest left x-value is -7. Notice it has a large open circle here that is not filled in. This means the function does not include -7 but includes numbers very close to it like-6.999999..... We sue use an inequality sign without an equal to to write -7. x >-7.
The furthest right x value is 9. It has a closed circle or "filled in" circle so we write with an equal to sign. [tex]x\leq 9[/tex].
We combine the two into [tex]-7<x\leq 9[/tex].
What is 2.45 x 10^4
A: 2450
B: 24,500
C: 245
D: 245,000
Answer:
I got B. 24,500 as my answer.
Step-by-step explanation:
2.45 x (10^4) = 24,500
The length of the poster is 16 inches. What is the length of this poster in centimeters. (1 inch = 2.54 centimeters)
Answer:
90
Step-by-step explanation:
Please answer this question!! 20 points and brainliest!
Answer:
A
Step-by-step explanation:
We can find the surface area of the object by adding the surface areas of each part. We have many rectangle faces to count and two triangular faces. Each has a formula for the area. We will find the area of each and then add them all together.
Triangle - 0.5 *b*h
Rectangle - b*h
Triangles
There are two triangles on either side. The height is 1.5. The base is 1.8.
0.5(1.5)(1.8)=1.35 meters squared
Since there are two, we will add 1.35+1.35 in our final calculation.
Rectangles
We will start by calculating the largest rectangle on the side. It has height of 4 and a base of 2.5 (shown above left).
4(2.5)=10
Since there are two (one we can see and one we can't), we will add 10+10 in our final calculation.
Next we calculate the top and bottom. The height is 3 and the base is 2.5 on top. But the bottom sticks out more and adds 1.8 to its base.
Top - 3(2.5)=7.5
Bottom-3(2.5+1.8)=12.9
Finally, we will calculate the front side and back(not visible) as well as the slant up front. The back side has height 4 and base 3. The front side has base 3 and height 4-1.5=2.5. The slant has base 2.3 and height 3.
Back - 4(3)=12
Front- 3(2.5)=7.5
Slant - 3(2.3)=6.9
We add all together for the total surface area: 1.35+1.35+10+10+7.5+12.9+12+7.5+6.9=69.5 meters squared.
Camp Oakes gets 32 juice boxes of orange juice and 56 boxes of apple juice each shelf in the cup board can hold eight boxes of juice what is the least number of cells needed for all the juice box
given f(x)=2^x, g(x) is found by translating f(x) three units right and two units down. Which function below shows g(x)?
[tex]\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis}[/tex]
[tex]\bf \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]
with that template in mind, let's check
C = -3, three units to the right
D = -2, two units down.
[tex]\bf f(x)=2^x~\hspace{10em}\stackrel{\stackrel{C=-3\qquad D=-2}{\cfrac{}{}}}{g(x)=2^{x-3}-2}[/tex]
Answer:
g(x) = 2^(x - 3) - 2.
Step-by-step explanation:
Translating 2^x 3 units to the right . This is done by changing it to 2^(x - 3). Then 2 units down is given by 2^(x -3) - 2.
Answer is 2^(x - 3) - 2.
Delany can run 1 1/2 of a mile at a rate 16 minutes and 30 seconds. At this rate how many minutes will it take him to run one mile?
Answer:
11 minutes
Step-by-step explanation:
Do 16 mins. 30 secs. divided by 1.5, since that is what you divide the miles by to get the base amount. The answer is 11 minutes.
Jonas is conducting an experiment using a 10-sided die. He determines that the theoretical probability of rolling a 3 is 1/10. He rolls the die 20 times. Four of those rolls result in a 3. Which adjustment can Jonas make to his experiment so the theoretical and experimental probabilities are likely to be closer?
A.) He can decrease the sample space.
B.) He can increase the sample space.
C.) He can decrease the number of trials.
D.) He can increase the number of trials.
Answer:
D. He can increase the number of trials.
Step-by-step explanation:
Jonas is conducting an experiment using a 10-sided die. So the theoretical probability of rolling a 3 in a single trial is, [tex]\dfrac{1}{10}[/tex]
So the theoretical expected outcome of 3 in 20 roll would be,
[tex]=\dfrac{1}{10}\times 20=2[/tex]
But when he rolled the die 20 times, where four of those rolls resulted 3.
Which is 2 times more than the theoretical expectation.
Increasing the number of trials from 20, the expected outcome will increase.
As the number of trials is multiplied with [tex]\dfrac{1}{10}[/tex], so bigger the number is from 20, bigger the value.
As we know,
[tex]E(x)=n\cdot P(x)[/tex]
If we want to increase the expected value, we have to increase the number of trials.
Answer with explanation:
Number of faces of this unique Die = 10
Theoretical probability of rolling a 3 [tex]=\frac{1}{10}[/tex]
Now, the die is rolled 20, times.
Number of times, the rolls results in 3= 4
Probability of rolling '3' [tex]=\frac{4}{20}=\frac{1}{5}[/tex]
but, if you roll the die twenty times, Probability of rolling '3' should be [tex]=\frac{2}{20}=\frac{1}{10}[/tex]
When we want, theoretical probability and experimental probability,match each other, the number of trials should be large enough to get closer and better results.
The adjustment can Jonas make to his experiment so the theoretical and experimental probabilities are likely to be closer:
D: He can increase the number of trials.
Lynn has 4 more books than Jose. If Lynn gives Jose 6 of her books, how many more will Jose have than Lynn?
he data set represents the number of miles Mary jogged each day for the past nine days.
6, 7, 5, 0, 6, 12, 8, 6, 9
The outlier of the data set is
Answer:
zero is your answer.
Step-by-step explanation:
Your answer for this question is 0
A 25-foot ladder is leaning against the side of a house. The top of the ladder is 20 feet above the ground. To the nearest degree, find the angle of elevation between the ground and the ladder.
To find the angle of elevation between the ground and the ladder, we can use the tangent function and the given measurements. The angle is approximately 39.8 degrees.
Explanation:To find the angle of elevation between the ground and the ladder, we can use trigonometry. Since the top of the ladder is 20 feet above the ground and the ladder is 25 feet long, we can use the opposite and adjacent sides of a right triangle. The trigonometric function that relates these sides is the tangent function:
tan(angle) = opposite/adjacent
Plugging in the known values, we get: tan(angle) = 20/25
Using a calculator to find the inverse tangent (arctan) of both sides, we get the angle to be approximately 39.8 degrees to the nearest degree.
Wally purchased a desk that was on sale do 2/3 of the original price. If the original price was $450, what was the price that Wally Paid?
Answer:
2/3 of 450 is 300 :)
RESPOND QUICK
Solve the first proportion for x. Use that value to solve the second proportion for
y. ,
x/24 = 9/72,
x/9 = y/12
A. x = 3, y = 4
B. x = 4, y = 3
C. x = 27, y = 36
D. x = 3, y = 6
Answer:
A
Step-by-step explanation:
3/24=9/72 3*3=9 24*3=72 x=3
3/9=y/12 9/3=3 12/3=4 y=4
X=3 y=4
A store makes shirts and jackets to sell each shirt costs $4 to make and each jacket costs $25 to make
Which expression is equal to (In picture)
[tex]3x^2+12x-15=3(x^2+4x-5)=3(x^2+5x-x-5)\\\\=3[x(x+5)-1(x+5)]=3(x+5)(x-1)\\----------------------\\4x^2+4x-8=4(x^2+x-2)=4(x^2+2x-x-2)\\\\=4[x(x+2)-1(x+2)]=4(x+2)(x-1)\\----------------------\\2x^2-8=2(x^2-4)=2(x^2-2^2)=2(x-2)(x+2)\\----------------------\\x^2-5x=x(x-5)\\----------------------\\\\\dfrac{3x^2+12x-15}{4x^2+4x-8}\cdot\dfrac{2x^2-8}{x^2-5x}\\\\=\dfrac{3(x+5)(x-1)}{4\!\!\!\!\diagup_2(x+2)(x-1)}\cdot\dfrac{2\!\!\!\!\diagup^1(x-2)(x+2)}{x(x-5)}\\\\\text{Canceled:}\ (x-1)\ \text{and}\ (x+2)[/tex]
[tex]=\boxed{\dfrac{3(x-2)(x+5)}{2x(x-5)}}[/tex]
suppose a normal distribution has a mean of 38 and a standard deviation of 2. What is the probability that a data value is between 36 and 43? Round your answer to the nearest 10th of a percent.
Answer:
83.5 %
Step-by-step explanation:
The mean is 38 and the standard deviation is 2
38 -2 is 36
36 is one standard deviation below the mean.
43 - 38 is 5
5/2 is 2 1/2 times the standard deviation above the mean
-1< z< 2.5
P ( Z<2.5 )−P (Z<−1 )
P ( Z<−1)=1−P ( Z<1 )
P ( Z<2.5 )-1+P ( Z<1 )
Using the standard normal table
0.9938 - 1 +0.8413
0.8351
83.51%
Rounding to the nearest tenth
83.5%
Yep the answer's 83.5%
godspeed in your adventures in cheating >:)
What is the midpoint of a segment whose endpoints are (9, −9) and (−3, 7)?
Answer:
The midpoint is (3,-1)
Step-by-step explanation:
The midpoint of a segment is found by adding the ends together and dividing by 2
midpoint = (x1+x2)/2 , (y1+y2)/2
=(9+-3)/2 , (-9+7)/2
= 6/2, -2/2
=3,-1