Answer:
From the given points above, the distance between them is 4 units.
Step-by-step explanation:
In order to find the distance between the two points, we must know the distance formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Now, we plug in our numbers from the coordinate points that we are given to their respectful places.
[tex]d=\sqrt{(8-8)^2+(8-4)^2}[/tex]
Now, we solve. First, simplify the terms in parentheses. So, subtract 8 from 8 and subtract 4 from 8.
[tex]d=\sqrt{(0)^2+(4)^2}[/tex]
Next, solve for the exponents.
[tex]d=\sqrt{0+16}[/tex]
Add the numbers in the radical.
[tex]d=\sqrt{16}[/tex]
Solve the radical.
[tex]d=4[/tex]
So, the distance between the two given points is 4 units.
Which expression is equivalent to the expression –6.4 – 12 + 4.6?
The answer is -13.8.
Hope this helps!
2065 Q.No. 2 a A firm produced 100 calculator sets during its first year. The total number of calculator sets produced at the end of five years is 4,500. Assume that the production increases uniformly each year. Estimate the increase in production each year. [3] Ans: 400
Answer:
400
Step-by-step explanation:
First, the firm produces 100 sets its first year. This means that our equation starts at 100. Next, the total number of calculator sets in 5 years is 4500. With y₁ representing the amount of calculator sets produced during year 1, y₂ representing the amount of sets during year 2, and so on, we can say that
y₁+y₂+y₃+y₄+y₅ = 4500
100 + y₂+y₃+y₄+y₅ = 4500
Next, we are given that the production increases uniformly by an amount each year. Representing that amount as a, we can say that
y₁+a = y₂
y₂+a = y₃
y₁+a+a = y₃
y₁+ 2 * a = y₃
and so on, so we have
100 + y₂+y₃+y₄+y₅ = 4500
100 + (100+a) + (100+2a) + (100+3a) + (100+4a) = 4500
500 + 10a = 4500
subtract 500 from both sides to isolate the a and its coefficient
4000 = 10a
divide both sides by 15 to isolate a
a = 400
Plz help me solve need help
Answer:
t=1, u=-2, w=-2
Step-by-step explanation:
Which solution value satisfies the inequality equation x – 5 ≤ 14?
Answer:
Any value that has x less than or equal to 19 is a solution
Step-by-step explanation:
x – 5 ≤ 14
Add 5 to each side
x – 5+5 ≤ 14+5
x ≤ 19
Any value that has x less than or equal to 19 is a solution
Answer:
[tex]\boxed{x\leq 19}[/tex]
Step-by-step explanation:
[tex]x-5\leq 14[/tex]
[tex]\sf Add \ 5 \ on \ both \ sides.[/tex]
[tex]x-5+5 \leq 14+5[/tex]
[tex]x\leq 19[/tex]
pls help :Find the missing side or angle.
Round to the nearest tenth.
Answer:
C° = 71.6056
Step-by-step explanation:
Law of Cosines: c² = a² + b² - 2abcosC°
Step 1: Plug in known variables
29² = 30² + 15² - 2(30)(15)cosC°
Step 2: Evaluate
841 = 900 + 225 - 900cosC°
-59 = 225 - 900cosC°
-284 = -900cosC°
71/225 = cosC°
cos⁻¹(71/225) = C°
C° = 71.6056
And we have our answer!
Answer:
79.0°
Step-by-step explanation:
The Law of Cosines is used for this purpose. It tells you ...
a² = b² +c² -2bc·cos(A)
Solving for A gives ...
cos(A) = (b² +c² -a²)/(2bc) = (15² +29²-30²)/(2(15)(29)) = 166/870
Using the inverse cosine function, we find the angle to be ...
A = arccos(166/870) ≈ 79.00026°
A ≈ 79.0°
To the nearest tenth, what is the area of the figure shown in the image? Segment BF is a line of symmetry of the pentagon ABCDE. Use 3.14 for pi. A. 30.3 in.^2 B. 33.0 in.^2 C. 39.3 in.^2 D. 48.3 in.^2 Please include ALL work! <3
Answer:
C, 39.3 in²
Step-by-step explanation:
Lets first find the area of the rectangle part of the house.
To find the area of a rectangle its base × height.
So its 6×4=24 in².
Now lets find the area of the top triangle.
Area for a triangle is (base × height)/2.
The height is 3 inches, because its 7-4. While the base is 6 inches.
(6×3)/2=9 in².
To find the area of the half circle the formula, (piR²)/2.
The radius of the circle is 2 because its half of the diamter which is 4.
(pi2²)/2=6.283 in².
Now we just need to add up the area of every part,
24+9+6.283=39.283in²
Select the correct answer. If , which statement is true? if g(x) = f(1/3x)
A. The graph of function f is stretched vertically by a scale factor of 3 to create the graph of function g.
B. The graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g.
C. The graph of function f is compressed horizontally by a scale factor of to create the graph of function g.
D. The graph of function f is compressed vertically by a scale factor of to create the graph of function g.
Answer:
B. The graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g.
Step-by-step explanation:
The rules for linear transformations are that
g(x) = a·f(b·(x-c)) +d
stretches the graph vertically by a factor of "a" (before the shift)
compresses the graph horizontally by a factor of "b" (before the shift)
shifts it to the right by amount "c"
shifts it up by amount "d".
Your equation has b=1/3, so the graph is compressed by a factor of 1/3, which is equivalent to a stretch by a factor of 3.
The appropriate choice of description is ...
b) the graph of g(x) is horizontally stretched by a factor of 3
Answer:
B
Step-by-step explanation:
Correct on Plato
Digits to write five hundred seven billion,six hundred forty million,seven hundred forty-two thousand,seventy two
Factor by grouping cd-9d-4c+36
Answer:
(d-4)(c-9)
Step-by-step explanation:
cd-9d-4c+36
d(c-9)-4(c-9)
pull out the (c-9),
(d-4)(c-9)
Please answer this correctly without making mistakes
Answer:
1/8
Step-by-step explanation:
3/8-1/8-1/8=1/8
Solve this problem:
5X +8 = 53
5X + 8 = 53
5X = 53 - 8
X = 45 / 5
X = 9
Answer:
X=9
Step-by-step explanation:
5X+8=53
To solve this we need to make X the subject of the equation that means X should be alone on one side of the equation. Taking the following steps
5X=53-8
5X=45
X=45/5
X=9
PLEASE ANSWER ASAP!!!
Fill in the box for the missing numerator in the set of equivalent expressions in the picture
Answer options are also shown in picture
any unrelated answer will be reported
Answer:
A. 14z - 28
Step-by-step explanation:
simplify z² - 3z
a. z(z - 3)
the denominator on the right has z(z - 3). but it is also multiplied by (z - 2)
this means the numerator must also be multiplied by (z - 2)
14 x (z - 2) = 14z - 28
hope this helps :)
A factory produces plate glass with a mean thickness of 4 mm and a standard deviation of 1.1 mm. A simple random sample of 100 sheets of glass is to be measured, and the mean thickness of the 100 sheets is to be computed. What is the probability that the average thickness of the 100 sheets is less than 3.74 mm
Answer:
0.0090483
Approximately = 0.00905
Step-by-step explanation:
z = (x - μ)/σ, where
x is the raw score = 3.74
μ is the sample mean = population mean = 4 mm
σ is the sample standard deviation
This is calculated as:
= Population standard deviation/√n
Where n = number of samples = 100
σ = 1.1/√100
σ = 1.1/10 = 0.11
z = (3.74 - 4) / 0.11
z = -2.36364
Using the z score table to determine the probability,
The probability that the average thickness of the 100 sheets is less than 3.74 mm
P(x<3.74) = 0.0090483
Approximately = 0.00905
Using the normal distribution and the central limit theorem, it is found that there is a 0.0091 = 0.91% probability that the average thickness of the 100 sheets is less than 3.74 mm.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means for size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean thickness of 4 mm, thus [tex]\mu = 4[/tex].Standard deviation of 1.1 mm, thus [tex]\sigma = 1.1[/tex].Sample of 100, thus [tex]n = 100, s = \frac{1.1}{\sqrt{100}} = 0.11[/tex].The probability is the p-value of Z when X = 3.74, then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3.74 - 4}{0.11}[/tex]
[tex]Z = -2.36[/tex]
[tex]Z = -2.36[/tex] has a p-value of 0.0091.
0.0091 = 0.91% probability that the average thickness of the 100 sheets is less than 3.74 mm.
A similar problem is given at https://brainly.com/question/14228383
Write a inequality.
Question: twice a number is no more than 14
Please help
Answer:
2x[tex]\leq[/tex]14
Step-by-step explanation:
Answer:
2x ≤ 14
Step-by-step explanation:
twice a number is no more than 14
2x ≤ 14
Robert has $20,000, part or all of which he wants to invest into a combination of government bonds and municipal bonds. He wants to invest no more than $5,000 into municipal bonds, and at least twice as much into government bonds than into municipal bonds.
Answer:
x + y ≤ 20,000y ≤ 5,000x ≥ 2yStep-by-step explanation:
Given:
Total amount = $20,000
Assume
Government bonds = x
Municipal bonds = y
Computation:
1. Invest total money
x + y ≤ 20,000
2. invest no more than $5,000 into municipal bonds
y ≤ 5,000
3. at least twice as much into government bonds.
x ≥ 2y
please help asap
Addition prop of equality
subtraction prop of quality
multiplication prop of equality
Division prop of equality
simplifying
distrib prop
Answer:
multiplication prop of equality, (multiplying both sides by 6)
simplifying, (not distrib prop as there is no parentheses)
Addition prop of equality, (adding 18 to each side)
simplifying
How are we supposed to find the Perimeter?
What function type does the table of values represent?
A) Linear
B) Exponential
C) Quadratic
D) Can't be determined
Answer:
Hello,
answer C
Step-by-step explanation:
[tex]\begin{array}{|c|c|c|c|}x&y&x^2&3x^2\\---&---&---&---\\1&3&1^2&3*1^2=3\\2&12&2^2&3*2^2=12\\3&27&3^2&3*3^2=27\\4&48&14^2&3*4^2=48\\5&75&5^2&3*5^2=75\\\end{array}\\\\\\\boxed{y=3x^2\ the\ function\ is\ quadratic.}[/tex]
URGENT, PLEASE HELP ! (2/5) - 50 POINTS - ! please no wrong answers for points. ! Which scatter plot represents the data?
Answer:
A has the points plotted correctly
Step-by-step explanation:
We need to plot the data
A has the points plotted correctly
B has the point ( 10,5) plotted on (9,5)
C is missing (-6,-5)
D is missing (-6,-5) and has (-2,1) instead of (-2,-1)
Answer:
A.
Step-by-step explanation:
It would be very helpful to write the points individually from the data. Take the x value and place it with its corresponding y value:
(1,4) ; (2,2) ; (-2,-1) ; (-2,-6) ; (5,-4) ; (-6,-5) ; (10,5)
Now find the graph that has each of these points. You can write these down and cross them out if you find them on the graph, and once you find the graph where all of these points are crossed out, that's the correct graph.
The correct graph is A.
:Done
x-(-4x-(y + y)); use x = -4, and y = -3 evaluate
please mark this answer as brainlist
2. If the diameter of a circle is 2V10, what is the area
of the circle.
Solve for x
A. 9
B. 10
C. 42
D. 12
Answer:
Option D, 12
Step-by-step explanation:
4x-8=80/2
or, 4x-8=40
or, 4x=48
or, x=12
Answer:
Given:-
m∠DEF= (4x-8) °
m DE= 80°
Using a property :- m ∠DEF= 1/2 (m DE)
[tex](4x-8)[/tex] ° [tex]= 1/2 (80)[/tex]
[tex](4x-8)[/tex]° [tex]=(40)[/tex] °
[tex]4x-8=40[/tex]
Add 8 to both sides:-
[tex]4x=48[/tex]
Divide both sides by 4:-
[tex]\frac{4x}{4}=\frac{48}{4}[/tex]
[tex]x=12[/tex]
OAmalOHopeO
A 7% acid solution will be mixed with a 15% acid solution. 20 L of a 12% acid solution needs to be made.
a) Use the varialbes defined in part a to create a system of linear equations that models the given situation. SHOW YOUR WORK .
b) How many litres of each solution are needed? SHOW YOUR WORK *
c) Verify the solution. SHOW YOUR WORK *
Answer:
see below
Step-by-step explanation:
Let r = amount of the 7% solution
y represent the amount of the 15 percent solution
.07r + .15 y = (r+y) .12
r+y = 20
y = 20-r
.07r + .15 (20-r) = (20) .12
0.07r+0.15(20-r)=2.4
.07r+ 3 - .15r = 2.4
-.08r = 2.4-3
-.08r = -.6
Divide by-.08
r =7.5 Liters of the 7%
y = 20-7.5
y = 12.5 L of 12%
Check
.07 *7.5 + .15 (12.5) =20*.12
.525+1.875=2.4
2.4=2.4
Simplify -3(2w - 6) +4(w + 1)
Answer:
= -2w + 22
Step-by-step explanation:
-3(2w - 6) + 4(w+1)
= (-3*2w -3*-6) + (4*w + 4*1)
= -6w + 18 + 4w + 4
= -6w + 4w + 18 + 4
= -2w + 22
round 1,965 to the nearest tenth
Step-by-step explanation:
1965 round to the nearest tenth is 1970
Answer:
1965.0
Step-by-step explanation:
In a large on-the-job training program, half of the participants are female and half are male. In a random sample of six participants, what is the probability that an investigator will draw at least one male?† (Round your answer to four decimal places.) P(X ≥ 1) =
Answer: 0.9844
Step-by-step explanation:
given data:
sample size n = 6
It’s assumed that half the population are male and the remaining half are females
F = 1/2
M = 1/2
the probability that the investigator would draw altleats one male
P ( x ≥ 1 ) =
= 1 - ( 0.5 ) ^ 6
= ( 0.5 )^6
= 0.9844
:) (8x2 + 7y2 – z2 + 2yz + 3xz - 5xy) (2x – 3y) slove this in vertical method
Step-by-step explanation:
8x² + 7y² - z² + 2yz + 3xz - 5xy
x 2x - 3y
-----------------------------------------------
-24x²y - 21y³ + 3yz² - 6y²z - 9xyz + 15xy²
+ 16x³ + 14xy² - 2xz² + 4xyz + 6x²z - 10x²y
-----------------------------------------------------------
16x³-21y³-34x²y+6x²z+29y²x-6y²z-2xz²+3yz²-5xyz
Please help quick !
Answer:
vertical angles
Step-by-step explanation:
Angle 1 and 3 are vertical angles. The angles are made from the same lines and share a vertex. They are opposite it each other
A general wishes to draw up his 7500 soldiers in the form of a square. After arranging, he found out that some of them are left out. How many soldiers were left out ?
If you want to form a square of 7500 soldiers, the side of the square must be [tex]\sqrt{7500}\approx86.6[/tex] soliders.
But since you cannot have 0.6 solider, the general needs to find the closest perfect square to the number 7500 which is less than 7500.
That number is 7396 which when square rooted gives 86 soliders on the side.
Subtract 7396 from 7500 and get how many soliders were left out,
[tex]7500-7396=\boxed{104}[/tex]
Hope this helps :)
In recent years, the interest rates on home mortgages have declined to less than 6%. However, a
recent study shows that the rate charged on credit card debt is more than 14%. A sample of 10 credit
cards showed that the mean rate charged is 15.64% with a standard deviation of 1.561%. At 1% level
of significance, is it reasonable to conclude the mean rate charged is greater than 14%?
Answer:
Yes it is reasonable to conclude the mean rate charged is greater than 14%
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 0.14[/tex]
The sample size is [tex]n = 10[/tex]
The sample mean is [tex]\= x = 0.1564[/tex]
The standard deviation is [tex]\sigma = 0.01561[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o: \mu = 0.14[/tex]
The alternative hypothesis is [tex]H_a : \mu > 0.14[/tex]
Generally the test statistic is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 0.1564 - 0.14 }{ \frac{0.01561 }{\sqrt{10} } }[/tex]
[tex]t = 3.322[/tex]
Now the p-value obtained from the z-table is
[tex]p-value = P(t > 3.322) = 0.00044687[/tex]
Since the [tex]p-value < \alpha[/tex] then we reject the null hypothesis, hence we can conclude that the mean rate charged is greater than 14%