9514 1404 393
Answer:
maybe
Step-by-step explanation:
It can be. It depends on the problem.
__
The rules of exponents are ...
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
Clearly, for division problems if the denominator exponent is larger, the difference 'b-c' will be negative.
__
You recall that an exponent is the way we show repeated multiplication.
x·x·x = x³
In division, like factors cancel, so ...
[tex]\dfrac{x\cdot x\cdot x}{x\cdot x}=\dfrac{x^3}{x^2}=\dfrac{x}{1}\cdot\dfrac{x\cdot x}{x\cdot x}=x^{3-2}=x^1=x[/tex]
Now, consider the same problem "upside down."
[tex]\dfrac{x\cdot x}{x\cdot x\cdot x}=\dfrac{x^2}{x^3}=\dfrac{1}{x}\cdot\dfrac{x\cdot x}{x\cdot x}=x^{2-3}=x^{-1}=\dfrac{1}{x}[/tex]
Paul writes newspaper articles. He earns a base rate of $500 per month and an additional $100 per article he writes. Last month he earned $2000.
Write an equation to determine the number of articles (a) he sold last month.
Answer:
Total earning last month with x articles is:
x*100 + 500This is same amount as 2000
The equation is:
100x + 500 = 2000Lisa bought a house The value of the house increased by 1.5% each year for 2 years. At the end of 2 years, the value of the house was £123,627. Work out the value of the house when Lisa bought it.
Answer:
$370,881
Step-by-step explanation:
firstly we we multiply 1,5% by 2yrs. the answer we get is 3,0%. we then multiply 3 % by $123,627 and get $370,881
If Lisa bought a house The value of the house increased by 1.5% each year for 2 years. The value of the house was £123,627. The initial amount of the house is 95120.7.
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
Given,
Lisa bought a house The value of the house increased by 1.5% each year for 2 years
By the end of 2 years, the value of the house was £123,627.
A=P(1+rt)
A is the final amount,
r is rate of interest
t is the time
P is principle amount.
123,627=P(1+1.5/100 (2))
123657=P(1+0.15(2))
123657=P(1+0.3)
123657=1.3P
Divide both sides by 1.3
P=95120.7
The initial amount of the house when Lisa bought is 95120.7
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Think of 5 positive integers that have a mode of 5 and 6, a median of 6 and a mean of 7.
Answer:
5,5,6,6,13
Step-by-step explanation:
Mode means most often. The 5 numbers has 2 modes 5 and 6
This means that 4 of the numbers must be 5,5,6,6
Median means the middle number must be 6
5,5,6,6,x is the only way to to get the middle number to be 6
We need to average to 7
(5+5+6+6+x) /5 = 7
(5+5+6+6+x) /5 *5= 7*5
(5+5+6+6+x) =35
22+x = 35
x = 35-22
x = 13
The other number is 13
Suppose triangle ABC is reflected over the x-axis. If the distance between point A and A’ is 14, what is the distance between the x-axis and A’.
1. 7
2. -7
3. 3.5
4. There is not enough information given.
Given:
The triangle ABC is reflected over the x-axis.
The distance between point A and A’ is 14.
To find:
The distance between the x-axis and A’.
Solution:
If a figure is reflected across the x-axis then the corresponding parts are mirror image of each other about the x-axis.
It means the distance between A and x-axis is same as the distance between x-axis and A'.
The distance between point A and A’ is 14.
Let d be the distance between the x-axis and A’. Then,
[tex]d+d=14[/tex]
[tex]2d=14[/tex]
[tex]d=\dfrac{14}{2}[/tex]
[tex]d=7[/tex]
Therefore, the correct option is 1.
A population has mean j = 18 and standard deviation o = 20. Find I, and oz for samples of size n = 100, Round your answers to
one decimal place if needed,
Answer:
))
Step-by-step explanation:
just place your decimal once to the left I think
can anyone help me and explain
Answer:
cf
=41
5 f-46
Step-by-step explanation:
thiis is the answer
Answer:
To find the inverse, switch the y(F(C)) and the x(C) variables.
So this function:
[tex]y=\frac{9}{5}x+32 \\[/tex]
Will become this function:
[tex]x=\frac{9}{5}y+32 \\[/tex]
You will then solve for y:
[tex]x=\frac{9}{5}y+32 \\x-32=\frac{9}{5}y\\5(x-32)=5(\frac{9}{5}y)\\5x-160=9y\\y=\frac{5x-160}{9}\\y=\frac{5x}{9}-\frac{160}{9}[/tex]
Substitute in the variables of this problem:
[tex]C(F)=\frac{5C}{9}-\frac{160}{9}[/tex]
The probability that a certain movie will win an award for acting is 0.15, the probability that it will win an award for direcing is 0.23, and the probability that it will win both is 0.09. Find the probabilities of the following.
a. The movie wins an award for acting, given that it wins both awards.
b. The movie wins an award for acting, given that it wins exactly one award.
c. The movie wins an award for acting, given that it wins at least one award.
Answer:
a) 0.15 / 0.09
b) 0.15 / 1
c) 0.15 / 0.23
A Roper survey reported that 65 out of 500 women ages 18-29 said that they had the most say when purchasing a computer; a sample of 700 men (unrelated to the women) ages 18-29 found that 133 men said that they had the most say when purchasing a computer. What is the 99% confidence interval for the difference of the two proportions
Answer:
[tex]Z=-2.87[/tex]
Step-by-step explanation:
From the question we are told that:
Probability on women
[tex]P(W)=65 / 500[/tex]
[tex]P(W) = 0.13[/tex]
Probability on women
[tex]P(M)=133 / 700[/tex]
[tex]P(M) = 0.19[/tex]
Confidence Interval [tex]CI=99\%[/tex]
Generally the equation for momentum is mathematically given by
[tex]Z = \frac{( P(W) - P(M) )}{\sqrt{(\frac{ \sigma_1 * \sigma_2 }{(1/n1 + 1/n2)}}})[/tex]
Where
[tex]\sigma_1=(x_1+x_2)(n_1+n_2)[/tex]
[tex]\sigma_1=\frac{( 65 + 133 )}{ ( 500 + 700 )}[/tex]
[tex]\sigma_1=0.165[/tex]
And
[tex]\sigma_2=1 - \sigma = 0.835[/tex]
Therefore
[tex]Z = \frac{( 0.13 - 0.19)}{\sqrt{\frac{( 0.165 * 0.835}{ (500 + 700) )}}}[/tex]
[tex]Z=-2.87[/tex]
Ms. Weaver plans to decorate the bulletin board in her classroom. She purchased 30 sheets of construction paper for $0.30 per sheet, 5 boxes of thumbtacks for $0.70 per box, and 4 framed pictures for $6.00 per picture. How much money did Ms. Weaver spend for the items?
Answer:
$36.5 money ms.weaver spent for the items
Please help
Find the value of x,
m∠5 = x-6, m∠4 = 2x+4, m∠2 = 2x-26
9514 1404 393
Answer:
x = 30 2/3
Step-by-step explanation:
Angles 4 and 5 are complementary, so we have ...
m∠4 +m∠5 = 90°
(2x +4) +(x -6) = 90
3x -2 = 90 . . . . . . . . . collect terms
3x = 92 . . . . . . . . . . add 2; next, divide by 3
x = 92/3 = 30 2/3
We are throwing darts on a disk-shaped board of radius 5. We assume that the proposition of the dart is a uniformly chosen point in the disk. The board has a disk-shaped bullseye with radius 1. Suppose that we throw a dart 2000 times at the board. Estimate the probability that we hit the bullseye at least 100 times.
Answer:
the probability that we hit the bullseye at least 100 times is 0.0113
Step-by-step explanation:
Given the data in the question;
Binomial distribution
We find the probability of hitting the dart on the disk
⇒ Area of small disk / Area of bigger disk
⇒ πR₁² / πR₂²
given that; disk-shaped board of radius R² = 5, disk-shaped bullseye with radius R₁ = 1
so we substitute
⇒ π(1)² / π(5)² = π/π25 = 1/25 = 0.04
Since we have to hit the disk 2000 times, we represent the number of times the smaller disk ( BULLSEYE ) will be hit by X.
so
X ~ Bin( 2000, 0.04 )
n = 2000
p = 0.04
np = 2000 × 0.04 = 80
Using central limit theorem;
X ~ N( np, np( 1 - p ) )
we substitute
X ~ N( 80, 80( 1 - 0.04 ) )
X ~ N( 80, 80( 0.96 ) )
X ~ N( 80, 76.8 )
So, the probability that we hit the bullseye at least 100 times, P( X ≥ 100 ) will be;
we covert to standard normal variable
⇒ P( X ≥ [tex]\frac{100-80}{\sqrt{76.8} }[/tex] )
⇒ P( X ≥ 2.28217 )
From standard normal distribution table
P( X ≥ 2.28217 ) = 0.0113
Therefore, the probability that we hit the bullseye at least 100 times is 0.0113
In what country of United states of heightlandia, the height measurements of ten year old children are approximately normally distributed with a mean of 53.2 inches and standard deviation of 6.7 inches?
Step-by-step explanation:
hi I can help you out in this work via Wazapp
The diagram below is divided into equal parts. Which fraction of the parts is white?
A diagram is divided into 4 blue parts and 3 white parts.
Three-sevenths
Four-sevenths
Three-fourths
Four-thirds
Answer: This problem is a fraction since we have several equal parts that make up one whole. The problem asks us to talk about the relationship of white pieces to the whole. Since we know the whole is made up of 7 pieces (4 blue parts and 3 white parts = 7 total parts), then 7 will be our denominator (number on the bottom of the fraction).
Now that we have our number on the bottom, we need to look back at the question to carefully decide what parts of the whole we are looking at. The question wants to know how many of the parts are white. We know that 3 of the parts are white, so that is our numerator (number of the top of the fraction).
Our final answer is 3/7 or "three-sevenths." Said another way, three of the seven pieces are white.
Step-by-step explanation:
Can someone help me please!!
What is the range of the given set of ordered pairs?
(9,-2) (4,3) ( 8, 10) (-4, 8)
Answer:
(-2,3,10,8)
Step-by-step explanation:
eg
(x,y)=(domain,range)
x components are domain and y components are range in the given set of ordered pairs
in the diagram below, BD is parallel to XY. what is the value of y?
a. 70
b. 130
c. 110
d. 20
I can't see the diagram sorry.
Step-by-step explanation:
Is there supposed to be a picture attached?
for the equation (x+3)(x+1)=1 explain why the solutions are not -3 and -1
Answer:
Step-by-step explanation:
(x+3)(x+1)=1
x²+3x+x+3=1
x²+4x+2=0
x²+4x+4=-2+4
(x+2)²=2
x+2=±√2
x=2+√2
and x=2-√2
so x≠-3
and x≠-1
Necesito ayuda con esto
Answer:
La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].
Step-by-step explanation:
Considerando que se tratan de dos matrices de igual dimensión y cuyos elementos son números reales, conocemos que la adición entre dos matrices consiste en las sumas de los elementos de igual posición, esto es, los elementos que están localizados en las mismas filas y columnas, entonces, la suma es:
[tex]\vec A = \left[\begin{array}{cc}1&2\\-1&0\end{array} \right][/tex], [tex]\vec B = \left[\begin{array}{cc}-2&9\\3&5\end{array}\right][/tex]
[tex]\vec U = \vec A + \vec B = \left[\begin{array}{cc}1 + (-2)&2+9\\-1 + 3&0 + 5\end{array}\right][/tex]
[tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex]
La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].
Which formula can be used to describe the sequence?
O f(x + 1) = f(x)
O f(x + 1) = - f(x)
O f(x) = f(x + 1)
O f(x) = - 3 f(x + 1)
Answer:
f(x+1) = -3/4 × f(x)
Step-by-step explanation:
first of all, the sign of the numbers in the sequence is alternating. so, there must be a "-" involved.
that eliminates the first and third answer options.
and the absolute values of the numbers in the sequence are going down. |f(x+1)| < |f(x)|
that eliminates the fourth answer option, as this says that
|f(x)| < |f(x+1)|. and that is the opposite of how the actual sequence behaves.
Verify that the equation is an identity.
Step-by-step explanation:
We need to prove that ,
cot x / csc x - csc x / cot x = - tan x sec x .
LHS :-
> cot x / csc x - csc x / cot x
> cos x / sin x ÷ csc x - sin x × csc x / cos x
> cosx - 1/ cos x
> cos² x - 1 / cos x
> - sin²x / cosx
> -sin x / cos x × sin x
> -tan x sin x
= RHS
Hence Proved !
Please help me on this real quick
Which figure can be formed from the net?
pls answer fast for brainiest !
Answer:
It should be the top right one
(with 6ft as the height)
Step-by-step explanation:
Answer:
It must be the lower to the left choice.
Step-by-step explanation:
As you can see, the net we have is composed of only triangles.
So we should be choosing a figure with a triangular base.
Our answers are narrowed down into the top right and lower left choices because both figures have triangular bases.
The other person down there chose the top right choice and was incorrect, so the answer should be the lower to the left figure.
Also, its the lower left figure because look at the triangular base, it is an isosceles meaning that two sides have the same length.
If the net says that the long side measures 9 ft, then the other two sides should be the same length and shorter than 9 ft. So the answer is the lower left figure.
Hope this helps
A study of the pay of corporate chief executive officers (CEOs) examined the increase in cash compensation of the CEOs of 104 companies, adjusted for inflation, in a recent year. The mean increase in real compensation was x¯=6.9%, and the standard deviation of the increases was s=55%. Is this good evidence that the mean real compensation μ of all CEOs increased that year? The hypotheses are
Answer:
The p-value of the test is 0.1017, which is greater than the standard significance level of 0.05, which means that this is not good evidence that the mean real compensation μ of all CEOs increased that year.
Step-by-step explanation:
At the null hypothesis, we test if there was no increase, that is, the mean is 0, so:
[tex]H_0: \mu = 0[/tex]
At the alternative hypothesis, we test if there was an increase, that is, the mean is greater than 0, so:
[tex]H_1: \mu > 0[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
104 companies, adjusted for inflation, in a recent year. The mean increase in real compensation was x¯=6.9%, and the standard deviation of the increases was s=55%.
This means that [tex]n = 104, X = 6.9, s = 55[/tex]
Value of the test-statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{6.9 - 0}{\frac{55}{\sqrt{104}}}[/tex]
[tex]t = 1.28[/tex]
P-value of the test:
The p-value of the test is a right-tailed test(test if the mean is greater than a value), with 104 - 1 = 103 df and t = 1.28.
Using a t-distribution calculator, this p-value is of 0.1017.
The p-value of the test is 0.1017, which is greater than the standard significance level of 0.05, which means that this is not good evidence that the mean real compensation μ of all CEOs increased that year.
The strength of one's immune system can be evaluated in several ways. One of the most popular methods involves measuring the concentration of adenosine triphosphate (ATP) in the blood. In women, the mean blood ATP level is 390 ng/mL, and the standard deviation is 115 ng/mL. It has been hypothesized that women with Major Depressive Disorder (MDD) have decreased immune function. A recent study found that a random sample of 30 women with MDD had an average blood ATP level of 355 ng/mL. Using a one-sample z test, what is the p-value of this result? (HINT: This involves a one-tailed hypothesis test).
Answer:
Hence the value of p is 0.04746.
Step-by-step explanation:
The test statistic is
[tex]Z=(\bar x-\mu)/(s/vn)\\\\=(355-390)/(115/ \sqrt(30))\\\\=-1.667[/tex]
The p-value= P(Z<-1.67) =0.04746. (from standard distribution table)
Therefore p-value =0.04746.
if a=(1 2 3 4) find A×A and the relation determined by (I) y=2x (II) x+y
Answer:
HOPE IT HELPS PLZ MARK ME BRAINLIEST
Step-by-step explanation:
A={1,2,3,4,5,6}
R={(x,y):y is divisible by x}
We know that any number (x) is divisible by itself.
(x,x)∈R
∴R is reflexive.
Now,(2,4)∈R [as 4 is divisible by 2]
But,(4,2)∈ /
R. [as 2 is not divisible by 4]
∴R is not symmetric.
Let (x,y),(y,z)∈R. Then, y is divisible by x and z is divisible by y.
∴z is divisible by x.
⇒(x,z)∈R
∴R is transitive.
Hence, R is reflexive and transitive but not symmetric.
A piece of wood is cut into three pieces in the ratio 6: 5: 2. If the log is 61/2 feet long, what will be the length of the longest piece
Answer:
14.077 feet to the nearest thousandth.
Step-by-step explanation:
First let's work out the multiplier:
6 + 5 + 2 = 13.
61/2 = 30.5
- so the multiplier is 30.5/13 = 2.34615
The longest piece refers to the 6 in the ratio its length
= 6 * 2.34615
= 14.0769 ft.
Simplify.
Rewrite the expression in the form 6^n6
n
6, start superscript, n, end superscript.
\dfrac{6^{4}}{6}=
6
6
4
Answer:
6^3
6 to the third power
or 3x3x3
Step-by-step explanation:
The solution of the expression 6⁻⁴.6⁶ will be 6².
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the expression is 6⁻⁴.6⁶. The expression will be solved as below:-
6⁻⁴.6⁶ = 6⁻⁴⁺⁶
Use the exponent property when the bases are the same then the powers will be added.
6⁻⁴.6⁶ = 6²
Therefore, the solution of the expression 6⁻⁴.6⁶ will be 6².
The complete question is to simplify the expression 6⁻⁴.6⁶.
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Exam grades: Scores on a statistics final in a large class were normally distributed with a mean of 75 and a standard deviation of 9. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least two decimals. (a) Find the 41st percentile of the scores. (b) Find the 74th percentile of the scores. (c) The instructor wants to give an A to the students whose scores were in the top 8% of the class. What is the minimum score needed to get an A
Solution :
Using the TI-84 PLUS calculator
a). Area : 0.41
μ = 75
σ = 9
InvNorm(0.41,75,9)
= 72.95209525
Therefore, the 41st percentile of the scores is 72.95209525
b). Area : 0.74
μ = 75
σ = 9
InvNorm(0.74,75,9)
= 80.79010862
Therefore, the 74st percentile of the scores is 80.79010862
c). 8%
So, Area : 0.92
μ = 75
σ = 9
InvNorm(0.92,75,9)
= 87.64564405
Therefore, X = 80.79010862
what is equivalent to x-2(3x-1)=3x
Answer:
1/4 = x
Step-by-step explanation:
x - 2( 3x - 1 ) = 3x
Step 1 :- Distribute 2
x - 2 × 3x - 2 × 1 = 3x
x - 6x + 2 = 3x
Step 2:- Combine like terms
-5x + 2 = 3x
Step 3 :- Add 5x to both sides
-5x + 5x + 2 = 3x + 5x
2 = 8x
Step 4 :- Divide both side by 8
2/8 = 8x / 8
1/4 = x
4
On a plan with a scale of 1:50, the floor of a rectangular cupboard is
shown with dimensions 25 cm by 3.6 cm. What are the actual dimensions
of the floor? Give your answers in metres.
Anyone know the answer ?
Answer:
The actual dimensions of the floor are 12,5m by 1,8m.
Step-by-step explanation:
Scale problems are solved by proportions, using a rule of three.
Scale of 1:50
This means that each cm on the cupboard has a real dimension of 50 cm
25 cm on the cupboard:
So the real dimension is:
25*50 = 1250 cm = 12,5m
3.6 cm
The real dimension is:
3.6*50 = 160 cm = 1,8 m
The actual dimensions of the floor are 12,5m by 1,8m.
