Answer:
x must be 13
Step-by-step explanation:
Represent the nine scores by a, b, c, d, e, f, g, h, i.
Write the following equation to indicate that the average of these nine scores is 8:
a+b+c+d+e+f+g+h+i
----------------------------- = 8, or a+b+c+d+e+f+g+h+i = 72 if we multiply both
9 sides of this equation by 9.
Next, we add scores x and x+ 1 to
a+b+c+d+e+f+g+h+i + x + x + 1
and divide the result by 11, as there are now 11 scores instead of just 9:
a+b+c+d+e+f+g+h+i + x + x + 1
----------------------------------------------
11
Earlier, we saw that a+b+c+d+e+f+g+h+i = 72. We can now replace
a+b+c+d+e+f+g+h+i in the above fraction by 72:
72 + 2x + 1
------------------- = 9 (as the new average is 9)
11
Multiplying both sides of this equation by 11 results in:
73 + 2x = 99, or 2x = 26.
Then x must be 13, and x + 1 must be 14.
Find the product: (6x+5)(2x−7)
Maria’s phone bills were $95, $67, $43, and $115. What was the mean, or average, of her phone bills?
Answer:
the mean is $80
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
Mean of Phone Bills =
[tex] \frac{phone \: bills \: total}{number \: of \: phone \: bills} \\ = \frac{95 + 67 + 43 + 115}{4} \\ = \frac{320}{4} \\ = 80[/tex]
Two people start biking from the same point. One heads east at 13 mph, the other south at 18 mph. What is the rate at which the distance between the two people is changing after 25 minutes and after 35 minutes? What is the rate at which the distance between the two people is changing after 25 minutes?
Answer:
[tex]22.21\ \text{mph}[/tex]
[tex]22.2\ \text{mph}[/tex]
Step-by-step explanation:
[tex]\dfrac{da}{dt}=13\ \text{mph}[/tex]
[tex]\dfrac{db}{dt}=18\ \text{mph}[/tex]
[tex]\dfrac{dc}{dt}[/tex] = Rate at which the distance between the two people is changing
At 25 minutes
[tex]a=13\times \dfrac{25}{60}=5.417\ \text{miles}[/tex]
[tex]b=18\times \dfrac{25}{60}=7.5\ \text{miles}[/tex]
[tex]c=\sqrt{5.417^2+7.5^2}\\\Rightarrow c=9.25\ \text{miles}[/tex]
Distance between the two people is
[tex]c^2=a^2+b^2[/tex]
Differentiating with respect to time we get
[tex]c\dfrac{dc}{dt}=a\dfrac{da}{dt}+b\dfrac{db}{dt}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{a\dfrac{da}{dt}+b\dfrac{db}{dt}}{c}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{5.417\times 13+7.5\times 18}{9.25}\\\Rightarrow \dfrac{dc}{dt}=22.21\ \text{mph}[/tex]
Distance between the two people is changing at a rate of [tex]22.21\ \text{mph}[/tex].
At 35 minutes
[tex]a=13\times \dfrac{35}{60}=7.583\ \text{miles}[/tex]
[tex]b=18\times \dfrac{35}{60}=10.5\ \text{miles}[/tex]
[tex]c=\sqrt{7.583^2+10.5^2}\\\Rightarrow c=12.95\ \text{miles}[/tex]
Distance between the two people is
[tex]c^2=a^2+b^2[/tex]
Differentiating with respect to time we get
[tex]c\dfrac{dc}{dt}=a\dfrac{da}{dt}+b\dfrac{db}{dt}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{a\dfrac{da}{dt}+b\dfrac{db}{dt}}{c}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{7.583\times 13+10.5\times 18}{12.95}\\\Rightarrow \dfrac{dc}{dt}=22.2\ \text{mph}[/tex]
Distance between the two people is changing at a rate of [tex]22.2\ \text{mph}[/tex].
help will give brainliest if right
BTW the last answer choice is D. 1
PLEASE DONT WASTE MY POINTS ITS THE 5TH TIME POSTING
An economist calculates that the cost of living in Westminster is currently $44,000 per year and is increasing by 5% per year. What will the cost of living be in 20 years? Round to the nearest cent.
Given:
Initial cost of living = $44,000
Rate of increase = 5% = 0.05
To find:
The cost of living in 20 years.
Solution:
The exponential growth model is:
[tex]y=a(1+r)^t[/tex]
Where, a is the initial value, r is the growth rate and t is the number of years.
Putting [tex]a=44000,r=0.05, t=20[/tex] in the above model, we get
[tex]y=44000(1+0.05)^{20}[/tex]
[tex]y=44000(1.05)^{20}[/tex]
[tex]y=116745.099026 [/tex]
[tex]y\approx 116745.10 [/tex]
Therefore, the cost of living in 20 years is about $116745.10.
What is the solution to the equation 2(x + 3)2 = 98?
Answer: if you're solving by x it would be x=43/2
Step-by-step explanation:
25 The library has an empty bookcase with 4 shelves. Each shelf can hold 23 chapter þooks. If the library has 117 new chapter books, how many will not fit on the bookcase?.
Answer:
25 chapter books
Step-by-step explanation:
117 - (23×4)
[23×4=92]
.°. 117 - 92 = 25
Step-by-step explanation:
Total Shelf Capacity = Capacity per shelf x Number of Shelves
= 23 x 4
= 92
Number of new books to be fit in = 117
Amount of books Overflow = Number of books to be fit in - Total Shelf Capacity
= 117 - 92
= 25
A graph of is shown on the grid.
What are the zeros of f?
Answer:
no graph is provided, the zeros of f cannot be found without a graph
Step-by-step explanation:
write 20.5×10^-5 in standard form. please help
Answer:
the answer is 2.05×10^-4
Tatiana has 894 flowers. She is making bouquets with 8 flowers in each bouquet. When she is done making all of the bouquets, how many flowers will she have left over? *
Answer:
6
Step-by-step explanation:
The remainder when 8 divides 894 is 6. So, she will be left with 6 flowers.
Solve the triangle using the Law of Sines. (Assume a = 7.1, b = 2.9, and ∠A = 70°. Round the length to one decimal place and the angles to the nearest whole number.)
Answer:
sides
a=7 (rounded)
b=3 (rounded)
c=8 (rounded)
angles
A=70
B=22.57
C=87.43
Step-by-step explanation:
a . given
b . given
c = a·sin(C)/sin(A)=7.54806
A . given
B = arcsin (b·sin(A)/a) = = 0.39393 rad = 22.57° = 22°34'13"
C = 180° - A - B = 1.52593 rad = 87.43° = 87°25'47"
Write a linear function f with f(2)=-2 and f(1)=1
Answer:
y = -3x + 4
Step-by-step explanation:
x y
0 4
1 1
2 -2
Going down 3 for every increase of x by 1, when x = 0, y = 4
Sonya randomly surveys 26 seventh graders to gather data about the amount of time spent each week using the Internet. Sonya records the data in the dot plot shown. What is the median of the data set?
What is the mean and the median
Answer:
You're lucky I have the dot plot, other wise this could not be answered.
Median: 7.5
Mean: 7.5
Yes, they are both 7.5.
Identify the transformation from figure A to figure B in the image below.
glide reflection
reflection
translation
dilation
Answer:
Reflection
Step-by-step explanation:
Here, we want to get the transformation that yielded figure B from figure A
Looking at the plot, we can see that we have the origin as the center of transformation
The kind of transformation however is reflection
The shape A was reflected about the origin or the point (0,0) to give shape B
Answer:
glide reflection
Step-by-step explanation:
got it right on a quiz
can someone please help me
Which quantity makes the equation true?
x + 3x + _______ = 7x
Answer:
Step-by-step explanation:
C) 3X
Answer: C. 3x
Step-by-step explanation:
Since x and 3x both have x, you can add them together to get 4x (if there is x by itself, it really means that there is one of it, so it would be 1x.)
Then, you subtract 7x by 4x, which gives you the answer, 3x. You could also solving it by asking yourself: What number plus 4x equals 7x, which would give you 3x.
The square root of 17 is between the what two whole numbers? (just list them with a comma in between them.)
Answer:
17 lies between 16 and 25. So√17 lies between √16 and √25. The prime factorization method is used to write a square root of a non-perfect square number in the simplest radical form.
Answer:
The answer is 16,25
Please help me i dont understand this
Answer:
209.3
Step-by-step explanation:
V=πr^2h / 3
= 3.14 x 25 x 8 /3
= 209.3
Please answer correctly !!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
2
Step-by-step explanation:
The scale factor is 2 because every aspect of figure a doubled.
Answer:
2Step-by-step explanation:
Figure B is 2 times the size of figure A
You can tell by counting the squares at the lines
Which expression is equivalent to
2x +3 - 3x + (-2)
A x + 5
B 12
12x - 1
x + 1
D 1 - 1
Answer:
-x + 1
Step-by-step explanation:
First, rewrite 2x +3 - 3x + (-2) as 2x +3 - 3x - 2. Note that +(-2) = -2.
Next, combine like terms. We get -x + 1.
Double check to determine whether this is one of the given possible answers.
A regular hexagonal prism has a base area of 84.3ft^2 and a Volume of 337.2ft^3. What is the height of the prism?
Answer:
Height = 4 ft
Step-by-step explanation:
Base are : 84.3 ft square
Volume : 337.2 square cuboid
Find the area of the following shapes.
Area of small rectange = 7 cm × 4 cm = 28 cm sq
Area of bigger rectangle = 4cm×10 cm = 40 cm sq
Area of traingle = 1/2 × 8*3 cm sq = 12 cm sq
total area of polygon = ( 28 + 40 + 12 ) cm sq
area of polygon = 80 cm sq
1 point
14. consider the polynomial
p(x) = 2x“ – (m + 3)x – 1.
If p(x) is divisible by x-2 then m=
Answer:
If [tex]p(x)[/tex] is divisible by [tex]x-2[/tex], then [tex]m = \frac{1}{2}[/tex].
Step-by-step explanation:
Let [tex]p(x) = 2\cdot x^{2}-(m+3)\cdot x - 1[/tex], if [tex]p(x)[/tex] is divisible by [tex]x-2[/tex], then [tex]p(2) = 0[/tex]. That is:
[tex]2\cdot 2^{2}-(m+3)\cdot (2)-1 = 0[/tex]
[tex]8 - 2\cdot m -6 -1 = 0[/tex]
[tex]1 -2\cdot m = 0[/tex]
[tex]2\cdot m = 1[/tex]
[tex]m = \frac{1}{2}[/tex]
If [tex]p(x)[/tex] is divisible by [tex]x-2[/tex], then [tex]m = \frac{1}{2}[/tex].
Determine which equation has the same solutions as the given equation.
x – 10k- 11=0
O A. (x-10)2 = 36
B. (x - 10)2 = 21
OC. (x - 5)2 = 21
OD. (x - 5)2 = 36
Answer:
D
Step-by-step explanation:
BRAINIEST TO WHIVER RIGHT HELP
Find the lateral surface 14ft area of the 2ft cylinder. Round your answer to the nearest tenth if necessary.
Answer:
616 square feet
Step-by-step explanation:
Lateral surface area of a cylinder can be determined by;
Lateral surface area = 2[tex]\pi[/tex]rh
where: r is its radius, and h is its height.
Given in the question that the height of the cylinder is 14 feet and of radius 2 feet, then;
Lateral surface area = 2[tex]\pi[/tex]rh
= 2 x [tex]\frac{22}{7}[/tex] x 2 x 14
= 2 x 22 x 2 x 7
= 616
Lateral surface area = 616 square feet
Thus, the lateral surface area of the cylinder is 616 square feet.
Evaluate the function
Answer:
92
Step-by-step explanation:
plug -4 into the function
3(-4)²-10(-4)+4
48+40+4
92
Answer:
92
Step-by-step explanation:
f(-4)=3(-4)^2-10(-4)+4
=3(16)-10(-4)+4
=48+40+4
=92
01. Apenas uma das matrizes abaixo é, ao mesmo tempo, quadrada, diagonal e identidade. Identifique-a: a[0,1,0,1]. B[1,0,0,1]. C[1,3,0,1]. D[1,1,1,1]. E[0,1,1,0]]
Responder:
b)
1 0
0 1
Explicação passo a passo:
Das opções fornecidas:
Todas as opções atendem à condição de uma matriz quadrada, pois todas têm o mesmo número de linhas e colunas (2 * 2)
Para ter uma matriz diagonal, todas as entradas fora da diagonal principal serão Zero.
Por outro lado, a matriz de identidade é um tipo especial de matriz quadrada com uma ao longo da diagonal principal.
Indo por essas condições apenas a matriz (b); atende às três condições.
What is the arc length of the shaded region of the circle to the newest centimeter?
Asking this again because the person who answered the last one gave the incorrect answer. If 7 iced cupcakes cost $21, then how much would 5 iced cupcakes cost?
Answer:
$15 for 5 cupcakes