Step-by-step explanation: 2+2=4 +4x8=9
what is the measure of the reference angle for a 102 degree angle? A. 78 degrees B. 68 degrees C. 57 degrees D. 12 degrees
Answer:
A. The reference angle measures 78 degrees
You deposit $4000 each year into an account earning 2% interest compounded annually. How much will you have in the account in 30 years?
The amount that will be in the account after 30 years is $162,272.32.
How much would be in the account after 30 years?When an amount is compounded annually, it means that once a year, the amount deposited and the interest already accrued increases in value. Compound interest leads to a higher value of deposit when compared with simple interest, where only the amount deposited increases in value once a year.
The formula that can be used to determine the future value of the yearly deposit of $4,000 in 30 years is : annuity factor x yearly deposit
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest raten = number of years$4000 x [{(1.02^30) - 1} / 0.02] = $162,272.32
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Find the root of the function f(x)=−4x+1.
Answer: A
Step-by-step explanation:
[tex]-\frac{4}{x}+1=0\\\\1=\frac{4}{x}\\\\x=4[/tex]
Which is the only state that uses to calculate its area
Answer:
The answer is circle.
Step-by-step explanation:
For all the rest of the shapes, we use certain base x height formulas. Square uses base x height along with parallelograms and trapezoids. For a triangle, we use [tex]\frac{base x height}{2}[/tex]. Though, for a circle, we use the formula [tex]\pi r^{2}[/tex] where r= radius.
Find the unit rate for each brand. Round to the nearest cent (hundredth).
The unit rate of each of the brands are:
Brand A's unit rate = 37 cents per ounce.
Brand B's unit rate = 31 cents per ounce.
How to Find the Unit Rate?The unit rate of each brand is simply how much a brand of tomatoes will cost per ounce.
To find the unit rate of each brand, do the following:
Brand A's unit rate = 2.99/8 = $0.37 per ounce = 37 cents per ounce.
Brand B's unit rate = 4.99/16 = $0.31 per ounce = 31 cents per ounce.
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A diver begins at 90 feet below sea level. She descends at a steady rate of 6 feet per minute for 6 minutes. Then, she ascends 20 feet. This expression shows her current depth in feet.
Negative 90 minus 6 (6) + 20
What is her current depth?
Negative 596 feet
Negative 556 feet
Negative 146 feet
Negative 106 feet
There are two bags containing only orange and red marbles. Bag A has 2 orange marbles and 6 red marbles. Bag B has 4 orange marbles and 16 red marbles. A marble is randomly chosen from each bag. List these events from least likely to most likely. Event 1: choosing an orange or red marble from Bag B. Event 2: choosing an orange marble from Bag B. Event 3: choosing an orange marble from Bag A. Event 4: choosing a purple marble from Bag A. Least likely Event Event, Event, X Most likely Event Ś ?
Answer:
From least to most likely:
Event 4, Event 2, Event 3, Event 1
Step-by-step explanation:
Event 1 has a 100% chance because there are only red and orange marbles in the bag.
In event 2, there are 4 orange marbles in the bag, giving us a (4/20) chance. This is 20%
In event 3, there are 2 orange marbles of 8 total, giving us an (2/8) chance. This is 25%
Lastly, there are no purple marbles in either bag, giving us a 0% chance of this occurring.
Which of the following expressions would simplify to be the multiplicative identity?
023.32
023.23
021
0 20
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ASK FOR HELP
The expression that would be simplified to be a multiplicative identity is 2^0
How to determine the expression that would be simplified to be a multiplicative identity?The complete question is added as an attachment
Multiplicative identities are represented as:
a * 1 = a
This means that the definition of multiplicative identities is the product of a number and 1
From the list of options, we have
2^0
When the exponent of a non-zero number is 0, the result is 1.
This means that
2^0 = 1
Hence, the expression that would be simplified to be a multiplicative identity is 2^0
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Three brothers, Jarek, Jerzy and Justyn, share a block of chocolate in the ratio of their ages. Jarek gets half of the bar. Jerzy gets 3\5 of the rest. Work out the ratio, in the form Jarek: Jerzy: Justyn, of how the brothers share the bar of chocolate.
Answer:
5:3:2
Step-by-step explanation:
see image
Jarek gets half. Then from the other half, Jerzy gets 3 pieces of 5 and Justyn gets the leftover 2 pieces. But Jarek's piece is all 5 pieces of the first half.
Jarek 5 parts:
Jerzy 3 parts:
Justyn 2 parts
5:3:2
see image
The tables show proportional relationships between x and y. Match each table with its constant of proportionality.
xy
1 10
2 20
3 30
xy
4 20
8 40
12 60
x y
2 15
4 30
6 45
4
12/04
10
xy
14
2 8
3 12
Give the opposite of each number. a. 3 b. –9 c. –5 d. 12 Solve each of the following problems. a. 9 + (–6) = ? b. (–5) + 8 = ? c. (–12) + (–6) = ? d. 10 – (–8) = ? e. (–4) – (+2) = ? f. –9 – (–5) = ? Solve each problem. Be sure to include the correct sign in your answer. a. 8 × 3 = ? b. –7 × 5 = ? c. –6 × (–9) = ? d. 8 ÷ (–2) = ? e. –24 ÷ (–3) = ? f. –36 ÷ 6 = ?
Answer:
Give the opposite of each number : a. -3; b. 9; c. 5; d. -12
Solve each of the following problems : a. 3; b. 3; c. -18; d. 18; e. -6; f. -4
Solve each problem. Be sure to include the correct sign in your answer :
a. 24; b. -35; c. 54; d. -4; e. 8; f. -6
Answer:
Step-by-step explanation:
1.a. –3
b. 9
c. 5
d. –12
2. a. 9 + (–6) = 3
b. (–5) + 8 = 3
c. (–12) + (–6) = –18
d. 10 – (–8) = 18
e. (–4) – (+2) = –6
f. –9 – (–5) = –4
3. a. 8 × 3 = 24
b. –7 × 5 = –35
c. –6 × (–9) = 54
d. 8 ÷ (–2) = –4
e. –24 ÷ (–3) = 8
f. –36 ÷ 6 = –6
5. Multiply the service charge by the number of months in a year.
12 × 7 = $84
Answer: $84 is deducted per year.
6. Add the balance of each year to determine the closing balance.
–$1500 + (–$1200) = –$2700
penn foster
Triangle ABC is defined by the points A(3,8), B(7,5), and C(2,3). Create an equation for a line passing through point A and perpendicular to BC.
The required equation for a line passing through point A and perpendicular to BC exists 2y + 5x = 31.
How to estimate the slope of the line?First, we must obtain the slope of the line perpendicular to BC
Given the coordinates B(7,5), and C(2,3)
Get the slope BC, exists
[tex]$m_{BC} = \frac{3-5}{2-7}[/tex]
= -2/-5 = 2/5
The slope of the line perpendicular to BC will be -5/2.
The slope of the required line in point-slope form exists expressed as;
[tex]$y - y_0 = m(x - x_0)[/tex]
m = -5/2
[tex](x_0, y_0) = (3, 8)[/tex]
Substitute the values into the formula we get
y - 8 = (-5/2)(x - 3)
2(y - 8) = (-5)(x - 3)
2y - 16 = (-5x + 15)
2y + 5x = 15 + 16
2y + 5x = 31
Therefore the required equation for a line passing through point A and perpendicular to BC exists 2y + 5x = 31.
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Find the slope and y-intercept of the line whose equation is y=6x=5
Answer:
the slope is 5 and the y intercept is 5
Step-by-step explanation:
I think that you meant to write y = 6x + 5.
y = mx + b
The number in in the m spot is the slope and the number in the b spot is the y intercept.
In the geometric pattern below, n represents the number of blocks in the bottom row of each figure.
n = 1
n=2
Write a function that models the total number of blocks in terms of n.
OA f(1) = 2; f(n) = f(n-1) + 2n; for n ≥ 2
OB. f(1) = 1; f(n) = f(n-1) + 2n; for n ≥ 2
Oc f(1) = 1; f(n) = f(n-1) + n; for n ≥ 2
OD. f(1) = 2; f(n) = f(n-1) + 4n; for n ≥ 2
n=3
Write out the sum. Do not evaluate.
∑∑k=1 (k^2-5k-3)[tex]4\\E(K^2-5k-3)\\k=1[/tex]
Series are sum of a given sequence.. The sum of the given expression is -33
Sequence and seriesSeries are sum of a given sequence. According to the given expression
∑∑k=1 (k^2-5k-3)
Taking the sum from k = 1 to k = 4
Sum = (1-5-3) + (4-10-3) +(9-15-3)+(15-20-3)
Sum = (-7) + (-9) + (-9) + (-8)
Sum = -33
Hence the sum of the given expression is -33
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Pizza prices by city (Data in Pizza prices) The company that sells frozen pizza to stores in four markets in the United States (Denver, Baltimore, Dallas, and Chicago) wants to examine the prices that the stores charge for pizza slices. Here are boxplots comparing data from a sample of stores in each market:
The answers to the questions are
a. No they are not the same
b. The presence of outliers are known to affect the market.
How to solve the box plot
For these areas we have
Q1 = 2.7 Q3 = 3 median = 2.8 out;ier 2.
Q1 = 2.5 Q3 = 2.7 median = 2.6 out;ier 3.1.
Q1 = 2.5 Q3 = 2.75 median = 2.65 out;ier 1.6
Q1 = 2.4 Q3 = 2.6 median = 2.5
We can see that the median prices in the markets are nearly similar except for the one that is conatined in the first market.
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Find the equation of a line with a slope of 13/2
that passes through the point (−2, — 10).
Answer: [tex]y=\frac{13}{2} x+3[/tex]
Step-by-step explanation:
Remember the point-slope equation which is [tex]y-y_{1} = m(x-x_{1} )[/tex] where[tex](x_{1} , y_{1} )[/tex] is your point and [tex]m[/tex] is your slope.
Given that we substitute what you have:
[tex]y-(-10) =\frac{13}{2} (x - (-2))[/tex]
Minus and minus give us positive:
[tex]y+10 =\frac{13}{2} (x +2)[/tex]
Multiply slope into the parenthesis:
[tex]y+10= \frac{13}{2}x + \frac{13}{2}*2\\[/tex]
Calculate it:
[tex]y+10= \frac{13}{2}x +13[/tex]
Isolate the [tex]y[/tex] by subtracting 10 from both sides:
[tex]y=\frac{13}{2} x + 13 -10[/tex]
Your final equation is:
[tex]y=\frac{13}{2} x +3[/tex]
Hope this makes sense!
And here's the graph to prove that the line actually goes through the point [tex](-2,-10)[/tex]:
Which rules define the function graphed below?
65
4
3
32
(0.2)
-2
-3-
(3,5)
--3--2--11 1 2 3 4
O y=x; y = 5
O y = x + 2; y = 5
O y=x; x = 5
O y=x+2; x = 5
The rules that define the piecewise function graphed are as follows:
y = x + 2, y = 5.
What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
In this problem, for x between 0 and 3, a linear function is given, with slope given as follows:
m = (5 - 2)/(3 - 0) = 1.
The y-intercept is of 2, as y = 2 when x = 0, hence the definition is:
[tex]y = x + 2, 0 \leq x \leq 3[/tex]
For x greater than 3, the function is constant at y = 5, hence the definition is:
y = 5, x > 3.
Hence, the rules that are used to define the piecewise function graphed are as follows:
y = x + 2, y = 5.
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Select the correct locations on the graph.
Select the lines that represent functions.
Answer:
(I've marked the lines considered functions with a check mark)
Step-by-step explanation:
which statement describes the function below
f(x)=x^3-x^2-9x+9
2x3 i think maybe yes
A scientist wants an 81milliliter of saline solution with a concentration of 5% she has concentrations of 3% and 9%. How much of each solution must she use to get the desired concentration
The quantity of each concentrations of 3% and 9% needed to get the desired concentration is 54 milliliters and 27 milliliters respectively
Simultaneous equationLet
Quantity of 3% needed = xQuantity of 9% needed = yx + y = 81
0.03x + 0.09y = 81 × 5%
0.03x + 0.09y = 4.05
x + y = 81
0.03x + 0.09y = 4.05
From (1)
x = 81 - y
Substitute into0.03x + 0.09y = 4.05
0.03(81 - y) + 0.09y = 4.05
2.43 - 0.03y + 0.09y = 4.05
- 0.03y + 0.09y = 4.05 - 2.43
0.06y = 1.62
y = 1.62/0.06
y = 27
substitute y = 27 intox = 81 - y
x = 81 - 27
x = 54
Simultaneous equation:
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Simplify the following fractions.
Please Slove this 2 question
Answer:
b)14/3 or 4 2/3 C) 256/15 or 14 1/15
Step-by-step explanation:
In the second fraction, the "of" means to multiply
Answer:
#b
[tex] \displaystyle{ \pmb{ \pink{3 \frac{1}{5} \times 3 \frac{1}{2} \div 2 \frac{2}{5} }}}[/tex]
[tex]\frak{SOLUTION:}[/tex]
[tex]\displaystyle \frak{Here,}[/tex]
[tex]\displaystyle{3 \frac{1}{5} \times 3 \frac{1}{2} \div 2 \frac{2}{5} }[/tex]
Convert mixed fractions into improper fractions:[tex] = \displaystyle{ \frac{16}{5} \times \frac{7}{2} \div \frac{12}{5} }[/tex]
[tex]=\displaystyle{ \frac{16}{5} \times \frac{7}{2} \times \frac{5}{12} \frak{(Performing division)} }[/tex]
[tex]\displaystyle{ = \frac{ \cancel{16} \: {}^{2} \times 7 \times \cancel5}{ \cancel5 \times \cancel 2 \times 12} }[/tex]
[tex]\displaystyle{ = \frac{8 \times 7}{12} }[/tex]
[tex] =\displaystyle{} \frac{56}{12} [/tex]
[tex]\displaystyle{ = \frac{ \cancel2 \times \cancel2 \times 2 \times 7}{ \cancel2 \times \cancel 2 \times 3} }[/tex]
[tex]\displaystyle{ = \frac{14}{3} \frak {\: or} \: 4 \frac{2}{3} } [/tex]
#c
[tex]\displaystyle{\pmb{ \pink{2 \frac{2}{3} \div \frac{1}{2} \: of \: 3 \frac{1}{5} }}}[/tex]
[tex]\displaystyle{ \frak{SOLUTION:}}[/tex]
[tex]\displaystyle \frak{Here,}[/tex]
[tex] \displaystyle{2 \frac{2}{3} \div \frac{1}{2} \: of \: 3 \frac{1}{5} }[/tex]
[tex]\displaystyle{ = \frac{8}{3} \div \left( \frac{1}{2} \times \frac{16}{5} \right)\frak{(Performing "of")}}[/tex]
[tex] = \displaystyle{ \frac{8}{3} \div \left( \frac{1 \times \cancel{16} \: {}^{8} }{ \cancel2 \times 5} \right) }[/tex]
[tex]\displaystyle{ = \frac{8}{3} \div \frac{8}{5} }[/tex]
[tex]\displaystyle{ = \frac{8}{3} \times \frac{5}{8} \frak{(Performing \: division)} }[/tex]
[tex]\displaystyle{ = \frac{ \cancel8}{3} \times \frac{5}{ \cancel8} }[/tex]
[tex] = \displaystyle{ \frac{5}{3} \frak{ \: or \: }1 \frac{2}{3} }[/tex]
Answered by :
[tex]\frak{\pink{seolleaphrodite}}[/tex]
Maria has 26 cars available to rent. Let C be the number of cars she would have left after renting R of them. Write an equation relating C to R. Then use this equation to find the number of cars she would have left after renting 23 of them.
Answer:
26 - R = C
3 cars
Step-by-step explanation:
26-R = C
26-23 = 3
A roller coaster’s height is given by the equation h = –.025t2 + 4t + 50, where t represents the time in seconds. How long will it take riders to pass over the hill and reach ground level? Hint: Set h = 0.
11.65 seconds
50.00 seconds
171.65 seconds
210.00 seconds
The time it will take the roller coaster to reach the ground is 171.65 seconds
Function and valuesGiven the roller coaster’s height given by the following parameters
h = –0.025t² + 4t + 50
On the ground level, the height will be zero. Substitute h = 0 and determine the value of t
–0.025t² + 4t + 50 = 0
0.025t² - 4t - 50 = 0
Factorize
On factorizing the time it will take the roller coaster to reach the ground is 171.65 seconds
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Solve for x if AB = 5x and BC = 3x + 24.
The value of x according to the given task is; 12.
What is the value of x?It follows from the task content that the value of x is to be determined.
Since, lines AB and BC are both tangent to the circle and they both share a point of intersection; it follows that;
5x = 3x +24
collect like terms2x = 24
divide both sides by 2x = 24/2
x = 12.
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Please help me solve this
If the sample mean is 51,sample size is 21 , sample standard deviation is 15 and confidence level is 95% then the lower bound is 45.35 and upper bound is 56.65.
Given sample mean of 51, sample size of 21, sample standard deviation be 15 and confidence level be 95%.
We are required to find the upper bound and lower bound.
We have to use t test as the sample size is less than 30.
Margin of error is the difference between calculated figures and real figures.
Margin of error= standard deviation* critical value of t
Critical value of t at 0.05 significance level with degree of freedom 20 [21-1] is 1.7247.
Margin of error=1.7247*15/4.5826
(4.5826 is the square root of 21)
=5.6454
Upper bound=51+5.6454
=56.6454
Lower bound=51-5.6454
=45.3546
After rounding off they will be 56.65 and 45.35.
Hence if the sample mean is 51,sample size is 21 , sample standard deviation is 15 and confidence level is 95% then the lower bound is 45.35 and upper bound is 56.65.
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The function g(x) is a transformation of the quadratic parent function, fx):
What function is g(x)?
90x)
15(x)
A. g(x) = 4x²
OB. g(x) = ² ->
O c. g(z) = -1¹
D. g(x)=-4x²
Answer: D
Step-by-step explanation:
The graph is narrower, so the coefficient of [tex]x^2[/tex] has an absolute value more than 1.
Eliminate B and C.Also, because g(x) opens down, the coefficient of [tex]x^2[/tex] is negative.
Eliminate A.This leaves D as the answer.
cual es el valor de 10=z-6
Answer:
z=16
Step-by-step explanation:
10=z-6
10+6=z-6+6
16=z
Answer:
10=z-6
or, z= 10+6
or, z = 16
the vale of y is 16
The graph below represents which of the following functions?
-12
-10
OA.
OB.
O C.
D.
4
F(x) =
[[|-*|× <1}
(x+4×21}
F(x) =
F(x) =
F(x) =
{/4-x²|x<2}
x2 2f
X
14-x²|x> 21
x x≤ 2}
2}
XS
{|-*² |× > 3)
(x+4× ≤3)
10
12
C
Answer: B
Step-by-step explanation:
The parabola has an open hole at x=2, and the line has a closed hole at x=2.
This means the top part of the function should have domain [tex]x < 2[/tex], and the second part of the function should have domain [tex]x \geq 2[/tex].
This eliminates everything except for B.
∫[tex]\frac{xdx}{(x^{2}+4)^{3} }[/tex]
Substitute [tex]u=x^2+4[/tex] and [tex]du=2x\,dx[/tex]. Then the integral transforms to
[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \int \frac{du}{u^3}[/tex]
Apply the power rule.
[tex]\displaystyle \int \frac{du}{u^3} = -\dfrac1{2u^2} + C[/tex]
Now put the result back in terms of [tex]x[/tex].
[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \left(-\dfrac1{2u^2} + C\right) = -\dfrac1{4u^2} + C = \boxed{-\dfrac1{4(x^2+4)^2} + C}[/tex]