Answer:
The original dimensions of the park are:
(23/2) yards by 7 yards.
Step-by-step explanation:
Suppose that you have a given dimension X
if you want to reduce that dimension by a scale factor k, such that:
0 < k < 1
The reduced dimension is just:
X' = k*X
Now let's solve the problem:
We know that the dimensions on the blueprint are:
(23/147)yd by (3/14)yd
And the original dimensions are:
A yd by B yd
We know that, to get the blueprint dimensions, we reduced the original dimensions by a factor of 2/147
Then we just have that:
(2/147)*A = 23/147
(2/147)*B = 3/14
Now we just can solve these two equations for A and B
A = (23/147)*(147/2) = 23/2
B = (3/14)*(2/147) = (3/7)*(1/147) = 49/7 = 7
Then the original dimensions of the park are:
(23/2) yards by 7 yards.
find all missing angles in the following diagram
Step-by-step explanation:
the item angle on the left line is also 130 degrees, as these 2 equally long lines create a triangle with 2 equal sides.
the two internal angles are the complement from 130 to 180 degrees, as every straight line stands for 180 degrees.
so, 180-130 = 50 degrees.
=> both internal angles are 50 degrees.
that makes the angle at the bottom tip of the triangle the complement of both 50 degree angle to 180, because the sum of all angles in a triangle is always 180 degrees.
so, 180 - 50 - 50 = 80 degrees.
and the outside angles of that triangle tip angle are each half of the complement of these 80 degrees to 180 (resistive to the bottom horizontal line).
180 - 80 = 100
100/2 = 50
so, both outside bottom angles are again 50 degrees.
The 2010 GSS provides the following statistics for the average years of education for lower-, working-, middle-, and upper-class respondents and their associated standard deviations. Assume that years of education are normally distributed in the population. Mean Standard Deviation N Lower-class 11.61 2.67 123 Working-class 12.80 2.85 697 Middle-class 14.45 3.08 626 Upper-class 15.45 2.98 38 How many years of education correspond to a Z score of +1.2 for upper-class respondents?
Answer:
The answer is "18.087 years".
Step-by-step explanation:
For upper class:
[tex]\mu=15.45 \ years\\\\\alpha=2.98 \ years\\\\[/tex]
[tex]P(Z \leq 1.2)[/tex] from the standard normal distribution on the table:
[tex]P(Z \leq 1.2) =0.8849\\\\x=z_{\alpha}+\mu\\\\[/tex]
[tex]=0.8849 \times 2.98 +15.45\\\\ = 2.637002+15.45 \\\\=18.087 \ \ years\\[/tex]
Find the mean of the following data set.
8, 5, 15, 12, 10
A. 12.5
B. 10
C. 14
D. 50
Answer:
10
Step-by-step explanation:
the sum of 8,5,15,12,10 is 50 and there are 5 numbers so 50 divided by 5 is 10 and it's mean is also 10
hope this helps !
Need help putting the answer in
Step-by-step explanation:
We can rewrite the given equation as
[tex]x^2 + \frac{1}{5}x - \frac{12}{25} = (x + \frac{4}{5})(x - \frac{3}{5})[/tex]
As a check, let's multiply out the factors:
[tex](x + \frac{4}{5})(x - \frac{3}{5}) = x^2 - \frac{3}{5}x + \frac{4}{5}x - \frac{12}{25}[/tex]
[tex]= x^2 + \frac{1}{5}x - \frac{12}{25}[/tex]
and this is our original equation.
If the smallest angle of a triangle is 20° and it is included between sides of 4 and 7, then (to the nearest tenth) the smallest side of the triangle is _____.
Answer:
[tex]3.5[/tex]
Step-by-step explanation:
The smallest side of a triangle is formed by the smallest angle in the triangle.
To find the side opposite (formed by) the 20 degree angle, we can use the Law of Cosines. The Law of Cosines states that for any triangle, [tex]c^2=a^2+b^2-ab\cos \gamma[/tex], where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are the three sides of the triangle and [tex]\gamma[/tex] is the angle opposite to [tex]c[/tex].
Let [tex]c[/tex] be the side opposite to the 20 degree angle.
Assign variables:
[tex]a\implies 4[/tex] [tex]b\implies 7[/tex] [tex]\gamma \implies 20^{\circ}[/tex]Substituting these variables, we get:
[tex]c^2=4^2+7^2-2(4)(7)\cos 20^{\circ},\\c^2=16+49-56\cos 20^{\circ},\\c^2=12.377213236,\\c=\sqrt{12.377213236}=3.51812638147\approx \boxed{3.5}[/tex]
Therefore, the shortest side of this triangle is 3.5.
Consider this function. f(x)-3x+3. Which graph represents the inverse of function f?
9514 1404 393
Answer:
graph Y
Step-by-step explanation:
The inverse function can be found by solving ...
x = f(y)
x = -3y +3
x -3 = -3y . . . . . subtract 3; next, divide by -3
y = -1/3x +1 . . . . . matches graph Y
_____
Additional comment
Writing the original equation in standard form can help you see its intercepts.
3x +y = 3
3x = 3 ⇒ x = 1 . . . . x-intercept (at y=0)
y = 3 . . . . y-intercept (at x=0)
The inverse function has the x- and y-intercepts swapped, so you're looking for a line through (0, 1) and (3, 0). The lower left graph (Y) is that graph.
Can someone please help me
Answer:
sorry I can't help you sorry
Answer:
c
Step-by-step explanation:
A reflection in the x- axis of the parent function is - [tex]\sqrt{x}[/tex]
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here the shift is 3 units up , then
g(x) = - [tex]\sqrt{x}[/tex] + 3
If $3000 is invested at 3% interest, find the value of the investment at the end of 7 years if the interest is compounded as follows. (Round your answers to the nearest cent.)
(i) annually
(ii) semiannually
(iii) monthly
(iv) weekly
(v) daily
(vi) continuously
Answer:
annualy=$3689.62
semiannually=$3695.27
monthly=$3700.06
weekly=$3700.81
daily=$3701.00
Continuously=$3701.03
Step-by-step explanation:
Given:
P=3000
r=3%
t=7 years
Formula used:
Where,
A represents Accumulated amount
P represents (or) invested amount
r represents interest rate
t represents time in years
n represents accumulated or compounded number of times per year
Solution:
(i)annually
n=1 time per year
[tex]A=3000[1+\frac{0.03}{1} ]^1^(^7^)\\ =3000(1.03)^7\\ =3689.621596\\[/tex]
On approximating the values,
A=$3689.62
(ii)semiannually
n=2 times per year
[tex]A=3000[1+\frac{0.03}{2}^{2(4)} ]\\ =3000[1+0.815]^14\\ =3695.267192[/tex]
On approximating the values,
A=$3695.27
(iii)monthly
n=12 times per year
[tex]A=3000[1+\frac{0.03}{12}^{12(7)} \\ =3000[1+0.0025]^84\\ =3700.0644[/tex]
On approximating,
A=$3700.06
(iv) weekly
n=52 times per year
[tex]A=3000[1+\frac{0.03}{52}]^3^6 \\ =3000(1.23360336)\\ =3700.81003[/tex]
On approximating,
A=$3700.81
(v) daily
n=365 time per year
[tex]A=3000[1+\frac{0.03}{365}]^{365(7)} \\ =3000[1.000082192]^{2555}\\ =3701.002234[/tex]
On approximating the values,
A=$3701.00
(vi) Continuously
[tex]A=Pe^r^t\\ =3000e^{\frac{0.03}{1}(7) }\\ =3000e^{0.21} \\ =3000(1.23367806)\\ =3701.03418\\[/tex]
On approximating the value,
A=$3701.03
if a x + B Y is equal to a square minus b square and b x + A Y is equal to zero find the value of x + Y
9514 1404 393
Answer:
a-b
Step-by-step explanation:
Add the two equations together:
(ax +by) +(bx +ay) = (a² -b²) +(0)
x(a +b) +y(a +b) = (a +b)(a -b)
x + y = a - b . . . . . divide by (a+b), assuming a+b ≠ 0
when solving 4x-3=5 the property used in the first step is the____ property of equality
Answer:
x = 2
Step-by-step explanation:
4x-3 + 3 = 5 + 3
4x = 8
4x ÷ 4 = 8 ÷ 4
x = 2
Hi there!
»»————- ★ ————-««
I believe your answer is:
"When solving 4x-3=5 the property used in the first step is the addition property of equality."
[tex]\boxed{x = 2}[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
We would 'undo' operations to solve for x. We would have to remove the '-3' first. Since the opposite of subtraction is addition, we would use the addition property of equality.⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x'....}}\\\\4x-3=5\\----------\\\text{\textbf{Addition Property of Equality:} Add three on both sides.}}\\\\\rightarrow 4x - 3 = 5 \\\rightarrow 4x -3 + 3 = 5 + 3\\\\\rightarrow \boxed{4x = 8}\\\\\text{\textbf{Division Property of Equality:} Divide both sides by 4.}}\\\\\rightarrow {4x=8}\\\rightarrow \frac{4x=8}{4}\\\\\rightarrow \boxed{x = 2}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
The graph shows the distance Liam traveled from school in miles (y) as a function of time in seconds (x). The graph is divided into four segments labeled P, Q, R, and S, respectively.
Graph shows 4 segments. Segment P is a horizontal straight line. Segment Q is a slanting straight line going up. Segment R is a slanting line going up. Segment S is a slanting straight line going down that touches the x-axis.
Which segment shows Liam waiting for a cab? (5 points)
Select one:
a. P
b. Q
c. R
d. S
Answer:
P
Step-by-step explanation:
Since we are looking at an f(x) graph where x is time and y is distance. Any time a graph is sloping we are either moving closer or further from the school. When there is a horizontal line, this means that there is no change in distance, thus Liam is waiting/standing still.
Answer:
a. P
Step-by-step explanation:
i took the test :)
Please help, been stuck on this for a while.
Answer:its blurry
Step-by-step explanation:
cant see it
Answer:
x = 34.6
Step-by-step explanation:
[tex]x\:=\:\frac{\left(20\cdot \:sin\left(60\right)\right)}{sin\left(30\right)}[/tex]
Based on the diagram, what is cos A?
Enter your answer in the boxes.
COS A=
[tex] cos(A) = \frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc} [/tex]
The cos A will be b/c
Cosine functionCosine function in a triangle is the ratio of the adjacent side to that of the hypotenuse
How to solve this problem?The steps are as follow:
Given,AB = c
BC = a
AC = b
AB is hypotenous whereas AC is adjacent side to AAccording to formula of cos,Cos A = Adjacent side to A / Hypoteneous
Cos A = AC / AB
Cos A = b / c
Therefore the value of Cos A in given figure will be b / c
Learn more about Cosine function here:
https://brainly.com/question/8120556
#SPJ2
Find the angle θ between ???? and ???? if ????⋅????=12‖????‖⋅‖????‖. (Use symbolic notation and fractions where needed. Give your answer in terms of π. )
Answer: hello your question is poorly written below is the complete question
Find the angle between and if ⋅=3√2‖‖⋅‖‖.
(Use symbolic notation and fractions where needed. Give your answer in terms of . )
answer :
∅ = π / 6
Step-by-step explanation:
V .W = [tex]\frac{\sqrt{3} }{2} || V ||. ||W||[/tex]
Hence
∅ = cos^-1 ( [tex]\frac{\frac{\sqrt{3} }{2} || V ||. ||W||}{||V||.||W||}[/tex]
∅ = cos^-1 ( [tex]\frac{\sqrt{3} }{2}[/tex] )
∴ ∅ = π / 6
pls help with all the questions
Answer:
Step-by-step explanation:
Since, CD is an altitude, ∠CDB will be a right angle.
m∠CDB = m∠CDA = 90°
By applying triangle sum theorem in ΔABC,
m∠CAB + m∠CBA + m∠ACB = 180°
20° + m∠CBA + 90° = 180°
m∠CBA = 180° - 110°
= 70°
Therefore, m∠CBD = 70°
By applying triangle sum theorem in ΔBCD,
m∠BCD + m∠CDB + m∠DBC = 180°
m∠BCD + 90° + 70° = 180°
m∠BCD + 160° = 180°
m∠BCD = 20°
m∠CAD = m∠A = 20°
m∠ACD = 90° - m∠BCD
= 90° - 20°
m∠ACD = 70°
16.7.1
One-fifth of the length of a foot-race is 7 miles. Find the length of the race.
Answer:
35 miles
Step-by-step explanation:
1/5 = 7
so each part is 7, which means that 5 parts would be 7*5.
7*5 = 35
cross check:
35/5 = 7
hope this helps :)
3. university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 4 hours. How large a sample must be selected if he wants to be 96% confident of finding whether the true mean differs from the sample mean by 2 hours
Answer:
A sample of 17 must be selected.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.96}{2} = 0.02[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.02 = 0.98[/tex], so Z = 2.054.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The standard deviation from a previous study is 4 hours.
This means that [tex]\sigma = 4[/tex]
How large a sample must be selected if he wants to be 96% confident of finding whether the true mean differs from the sample mean by 2 hours?
A sample of n is required.
n is found for M = 2. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = 2.054\frac{4}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 2.054*4[/tex]
Simplifying both sides by 2:
[tex]\sqrt{n} = 2.054*2[/tex]
[tex](\sqrt{n})^2 = (2.054*2)^2[/tex]
[tex]n = 16.88[/tex]
Rounding up:
A sample of 17 must be selected.
Plz help. I’m finding surface area. I need the answer in units. Thank you.
Answer:
C. 17 units
Step-by-step explanation:
Surface area of rectangular prism is given as:
A = 2lw + 2lh + 2wh
A = 930 square units
l = 12 units
h = 9 units
w = ? (We're to find the width)
Plug in the value into the formula
930 = 2*12*w + 2*12*9 + 2*w*9
930 = 24w + 216 + 18w
Add like terms
930 - 216 = 42w
714 = 42w
Divide both sides by 42
714/42 = 42w/42
17 = w
w = 17 units
Question 1 of 10
The triangles shown below may not be congruent.
66V
100
100
00
2017
A. True
B. False
SUBMIT
Answer:
A. TRUE
Step-by-step explanation:
To determine if two triangles are congruent, we need to establish the facts that the three angles and three side lengths of one is congruent to corresponding angles and side lengths of the other triangle.
The diagram given only tells us the angle measure of the two triangles which are congruent to each other. The side length wasn't given. Therefore, the triangles may not be congruent.
I need help answering this question.
Answer:
hello dude
x - 9 = - 12
x = 9 -12
x = -3
HAVE A NİCE NİGHT
Step-by-step explanation:
Greetings from Turkey
We have to,
find the required value of x.
Let's start,
→ x - 9 = -12
→ x = -12 + 9
→ x = -3
Thus, -3 is the value of x.
for the function f(x)=5 evaluate and simplify the expression: f (a+h)-f(a)/h
Answer:
0 is the answer assuming the whole thing is a fraction where the numerator is f(a+h)-f(a) and the denominator is h.
Step-by-step explanation:
If the expression for f is really a constant, then the difference quotient will lead to an answer of 0.
If the extra for f is linear (including constant expressions), the difference quotient will be the slope of the expression.
However, let's go about it long way for fun.
If f(x)=5, then f(a)=5.
If f(x)=5, then f(a+h)=5.
If f(a)=5 and f(a+h)=5, then f(a+h)-f(a)=0.
If f(a+h)-f(a)=0, then [f(a+h)-f(a)]/h=0/h=0.
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
I really need help on this
a) B
b) D
Hope this helps you
Yess again pls help!
Tyyy
what is the approximate value of x in the diagram below?
Answer:
Where is the diagram though..
Step-by-step explanation:
Say you buy halibut at $19 per pound . One portion of seared halibut requires 6 ounces of halibut . How much does the halibut for one portion cost ? Round to the nearest cent .
Answer:
$7.13
Step-by-step explanation:
Given data
Cost of halibut per pound= $19
Let us convert pound to ounces first
1 pound = 16 ounces
Hence 16 ounces will cost $19
6 ounces will cost x
cross multiply we have
x= 19*6/16
x=114/16
x=$7.13
Hence 6 ounces will cost $7.13
Keisha borrowed $400 from a bank for 5 years and was charged simple interest. The total interest that she paid on the loan was $120. As a percentage, what was the annual interest rate of her loan?
Answer:
6%
Step-by-step explanation:
Answer:
you need to divide 120 by 5
Step-by-step explanation:
the percentage is 16.6 and it goes on that is for 1 year
4 mangoes and Pears cost $24 while to Mangos in three pears cost $16. Write a pair of simulataneous equations in x and y to represent the information given. State clearly what x and y represent
Answer:
x- cost of mango, y- cost of pear, 4x+4y=24 and 2x+3y=16
Step-by-step explanation:
For this, you first must assign variables. In this case, let's say x is the cost of a mango and y is the cost of a pear.
Therefore the total cost for the first part can be given by 4x+4y=24.(or 4 × the cost of a mango + 4 × the cost of a pear = $24).
Following this method, the second equation can be given by 2x+3y=16.
** building upon this knowledge (extension)**
To solve simultaneous equations, we need like terms. To make like terms, we can multiply the entire second equation by 2. This gives 2 equations of 4x+4y=24 and 4x+6y=32.
We solve this by subtracting one equation from another, giving (4x-4x)+(6y-4y)=(32-24), or 2y=8.
We can divide by 2 to get y=4, meaning a pear costs $4.
By substituting y with 4, we can work out x. 4x+4×4=24, also known as 4x+16=24.
We can subtract 16 to get 4x=8, and divide by 4, giving x=2, or a mango costs $2.
**This content involves writing simultaneous equations, which you may wish to revise. I'm always happy to help!
Decide which of the two given prices is the better deal and explain why.
You can buy shampoo in a 5-ounce bottle for 3,89$ or in a 14-ounce bottle for 11,99$.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.The -ounce bottle is the better deal because the cost per ounce is $
nothing per ounce while the -ounce bottle is $
nothing per ounce.
B.The -ounce bottle is the better deal because the cost per ounce is $
nothing per ounce while the -ounce bottle is $
nothing per ounce.
(Round to the nearest cent as needed.)
Answer:
The 14-ounce bottle is the better deal
Step-by-step explanation:
I know this beause inorder to figure out which one is better you have to make them the same price and then see which bottle has more ounces. So I made each price 1$ so there is 1.58-ounces per dollar in the 5-ounce bottle and 1.17 -ounces per dollar in the 14-ounce bottle.
Suppose that you are interested in determining the average height of a person in a large city. You begin by collecting the heights of a random sample of 196 people from the city. The average height of your sample is 68 inches, while the standard deviation of the heights in your sample is 7 inches. The standard error of your estimate of the average height in the city is
Answer:
The standard error of your estimate of the average height in the city is 0.5 inches.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
You begin by collecting the heights of a random sample of 196 people from the city.
This means that [tex]n = 196[/tex]
The standard deviation of the heights in your sample is 7 inches.
This means that [tex]\sigma = 7[/tex]
The standard error of your estimate of the average height in the city is
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{7}{\sqrt{196}} = 0.5[/tex]
The standard error of your estimate of the average height in the city is 0.5 inches.