Answer:
(8,6)Step-by-step explanation:
g(x) = |x – 8| + 6 was transformed from the parent function g(x) = |x|:
8 unit right
6 units up
a parent absolute value function has a vertex at (0,0)
if the function is moved so is the vertex:
(0+8,0+6)
(8,6)
So, the vertex of this function is at (8,6)
Answer: vertex = (8, 6)
Step-by-step explanation:
The Vertex form of an absolute value function is: y = a|x - h| + k where
a is the vertical stretch(h, k) is the vertexg(x) = |x - 8| + 6 is already in vertex form where
h = 8 and k = 6
so the vertex (h, k) = (8, 6)
Select the type of equations. Consistent. Equivalent. Inconsistent
Answer:
Consistent.
Step-by-step explanation:
Since there is one solution ( the lines intersect), the equations are consistent
They would be inconsistent if the lines do not intersect
The would be equivalent if they are the same line
The answer would be consistent.
Step-by-step explanation:
In the graph shown here, there is only one solution
because the lines intersect at the point (5, 3).
In order for the lines to be inconsistent, the lines would have to not
meet or intersect each other but notice that this is not the case here.
The would be equivalent if they are the same exact line
so it would look like there would just be one line.
slope=4/3 find the equation of the parallel line through (5,5)
Answer:
[tex]y=\frac{4}{3}x-1.75[/tex]
Step-by-step explanation:
If the slope of a line is 4/3,
and we wanna find the equation of a line that is parallel to it and crosses through (5,5).
So we already have the slope because the slope of 2 parallel lines are the same.
y = 4/3x
Look at the image below↓
So now we just need to find the y-intercept.
After some numbers we got,
[tex]y=\frac{4}{3}x-1.75[/tex]
Look at the other image below↓
Thus,
the equation of the parallel line is [tex]y=\frac{4}{3}x-1.75[/tex].
Hope this helps :)
Find X.
Round to the nearest tenth.
Law of Cosines : c2 = 22 + b2 - 2ab cos C
Answer:
70.5°
Step-by-step explanation:
22² = (20)²+(18)² - 2(20)(18) cos X
484 = 400 + 324 - 720 cos X
-240 = -720 cosx
1/3 = cos X
[tex]cos^{-1}(\frac{1}{3})[/tex] = X
X = 70.52877937
A basketball coach is curious about the heights of players in the league. Let the proportion of basketball players who are over 72 inches be p. If the coach wanted to know if the proportion of basketball players who are over 72 inches is more than 85%, what are the null and alternative hypothesis? Select the correct answer below: H0: p=0.85; Ha: p<0.85 H0: p>0.85; Ha: p=0.85 H0: p=0.85; Ha: p>0.85 H0: μ=0.85; Ha: μ>0.85
Answer:
H0: p=0.85;
Ha: p>0.85
Step-by-step explanation:
What was being tested is that:
the coach wanted to know if the proportion of basketball players who are over 72 inches is more than 85%.
The null hypothesis which we are testing against would be that the proportion of basketball players who are over 72 inches is 85%.
H0: p=0.85;
Ha: p>0.85
Need help with graphing
An experiment involves 17 participants. From these, a group of 3 participants is to be tested under a special condition. How many groups of 3 participants can
be chosen, assuming that the order in which the participants are chosen is irrelevant?
Answer: 680
Step-by-step explanation:
When order doesn't matter,then the number of combinations of choosing r things out of n = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Given: Total participants = 17
From these, a group of 3 participants is to be tested under a special condition.
Number of groups of 3 participants chosen = [tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\[/tex]
[tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\\\\=\dfrac{17\times16\times15\times14!}{3\times2\times14!}\\\\=680[/tex]
Hence, there are 680 groups of 3 participants can be chosen,.
Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, and then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Among 2160 passenger cars in a particular region, 243 had only rear license plates. Among 358 commercial trucks, 55 had only rear license plates. A reasonable hypothesis is that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a 0.05 significance level to test that hypothesis. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval.
Answer:
For 0,90 of Confidence we reject H₀
For 0,95 CI we reject H₀
Step-by-step explanation:
To evaluate a difference between two proportion with big sample sizes we proceed as follows
1.-Proportion 1
n = 2160
243 had rear license p₁ = 243/2160 p₁ = 0,1125
2.Proportion 2
n = 358
55 had rear license p₂ = 55/ 358 p₂ = 0,1536
Test Hypothesis
Null Hypothesis H₀ ⇒ p₂ = p₁
Alternative Hypothesis Hₐ ⇒ p₂ > p₁
With signficance level of 0,05 means z(c) = 1,64
T calculate z(s)
z(s) = ( p₂ - p₁ ) / √ p*q ( 1/n₁ + 1/n₂ )
p = ( x₁ + x₂ ) / n₁ + n₂
p = 243 + 55 / 2160 + 358
p = 0,1183 and then q = 1 - p q = 0,8817
z(s) = ( 0,1536 - 0,1125 ) / √ 0,1043 ( 1/ 2160 + 1 / 358)
z(s) = 0,0411 /√ 0,1043*0,003256
z(s) = 0,0411 / 0,01843
z(s) = 2,23
Then z(s) > z(c) 2,23 > 1,64
z(s) is in the rejection region we reject H₀
If we construct a CI for 0,95 α = 0,05 α/2 = 0,025
z (score ) is from z- table z = 1,96
CI = ( p ± z(0,025*SE)
CI = ( 0,1536 ± 1,96*√ 0,1043*0,003256 )
CI = ( 0,1536 ± 1.96*0,01843)
CI = ( 0,1536 ± 0,03612 )
CI = ( 0,11748 ; 0,18972 )
In the new CI we don´t find 0 value so we have enough evidence to reject H₀
A random sample of 64 students at a university showed an average age of 20 years and a sample standard deviation of 4 years. The 90% confidence interval for the true average age of all students in the university is
Answer:
The 90% confidence level is [tex]19.15< L < 20.85[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 64[/tex]
The mean age is [tex]\= x = 20 \ years[/tex]
The standard deviation is [tex]\sigma = 4 \ years[/tex]
Generally the degree of freedom for this data set is mathematically represented as
[tex]df = n - 1[/tex]
substituting values
[tex]df = 64 - 1[/tex]
[tex]df = 63[/tex]
Given that the level of confidence is 90% the significance level is mathematically evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha =[/tex]10 %
[tex]\alpha = 0.10[/tex]
Now [tex]\frac{\alpha }{2} = \frac{0.10}{2} = 0.05[/tex]
Since we are considering a on tail experiment
The critical value for half of this significance level at the calculated degree of freedom is obtained from the critical value table as
[tex]t_{df, \frac{ \alpha}{2} } = t_{63, 0.05 } = 1.669[/tex]
The margin for error is mathematically represented as
[tex]MOE = t_{df , \frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 1.699 * \frac{4 }{\sqrt{64} }[/tex]
[tex]MOE = 0.85[/tex]
he 90% confidence interval for the true average age of all students in the university is evaluated as follows
[tex]\= x - MOE < L < \= x + E[/tex]
substituting values
[tex]20 - 0. 85 < L < 20 + 0.85[/tex]
[tex]19.15< L < 20.85[/tex]
what is the length of a hypotenuse of a triangle if each of its legs is 4 units
Answer:
[tex]\boxed{c = 5.7 units}[/tex]
Step-by-step explanation:
Using Pythagorean Theorem:
=> [tex]c^2 = a^2+b^2[/tex]
Where c is hypotenuse, a is base and b is perpendicular and ( a, b = 4)
=> [tex]c^2 = 4^2+4^2[/tex]
=> [tex]c^2 = 16+16[/tex]
=> [tex]c^2 = 32[/tex]
Taking sqrt on both sides
=> c = 5.7 units
Answer:
5.65 unitsStep-by-step explanation:
Given,
Base ( b ) = 4 units
Perpendicular ( p ) = 4 units
Hypotenuse ( h ) = ?
Now,
Using Pythagoras theorem to find length of hypotenuse:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
Plugging the values
[tex] {h}^{2} = {4}^{2} + {4}^{2} [/tex]
Evaluate the power
[tex] {h}^{2} = 16 + 16[/tex]
Calculate the sum
[tex] {h}^{2} = 32[/tex]
[tex]h = \sqrt{32} [/tex]
[tex]h = 5.65 \: units[/tex]
Hope this helps..
Best regards !!
Suppose you just flipped a fair coin 8 times in a row and you got heads each time! What is the probability that the next coin flip will result in a heads
Answer:
The probability is 1
Step-by-step explanation:
Given
Number of flips = 8
Outcomes = 8 heads
Required
Probability of getting a head in the next row
This problem can be attributed to experimental probability and it'll be solved using experimental probability formula, which goes as follows;
[tex]Probability = \frac{Number\ of\ Occurence}{Total\ Trials}[/tex]
Let [tex]P(Head)[/tex] represents the probability of getting a head in the next row;
[tex]P(Head)= \frac{Outcome\ of\ head}{Total\ Flips}[/tex]
[tex]P(Head)= \frac{8}{8}[/tex]
[tex]P(Head)= 1[/tex]
Hence, the probability of obtaining a head in the next flip is 1
what is the domain and range of the relation shown?
Answer:
A.
{-4 ≤ x ≤ 4}
{-4 ≤ y ≤ 4}
Step-by-step explanation:
We’ll domain is the amount of x values,
Range is the amount of y values
_______________________________
Domain:
Starts from -4 to 4
{-4 ≤ x ≤ 4}
I made the sign less than or equal to because the circle lines are solid.
Range:
This starts from -4 to 4 also.
{-4 ≤ y ≤ 4}
Thus,
answer choices A. is correct
Hope this helps :)
Hey there! I'm happy to help!
Note that this is not a function because some inputs can have more than one output, that's why they say relation, not function! :D
DOMAIN
The domain is all of the possible x-values of the relation. We see that the lowest x-value is -4, while the highest is 4. If you plug in these two or any number in between, there will be at least one corresponding output.
This domain can be written as -4 ≤ x ≤ 4.
RANGE
The range is all of the possible outputs or y-values. We see that the minimum y-value is -4 and that the highest is 4. Therefore, we will just write it the same as the domain but use a different variable.
-4 ≤ y ≤ 4.
This matches with Option A.
I hope that this helps! Have a wonderful day!
In the news, you hear “tuition is expected to increase by 7% next year.” If tuition this year was $1200 per quarter, what will it be next year?
Answer: $1284 per quarter
Step-by-step explanation:
Answer:
$5136
step by step:
this year tuition-1200
in a year there are 4 quarters
so total this yr is 1200×4=4800
Next year
tuition is 100%+7%per 4months
so
1.07×1200=1284per month
per year 1284×4=5136
Pick two cards at random from a well-shuffled deck of 52 cards (pick them simultaneously so they are not the same card). There are 12 cards considered face cards. There are 4 cards with the value 10. Let X be the number of face cards in your hand. Let Y be the number of 10's in your hand. Explain why X and Y are dependent.
Answer:
The variables X and Y are dependent.
Step-by-step explanation:
The variable X denotes number of face cards . That is it can take values,
X = {0, 1, 2 }
Compute the probability for all he values of X as follows:
P [X = 0] = P (None of the 12 card is chosen in either draw)
= (40/52)×(39/51)
= 1560/2652
= 0.5882
P [X = 1] = P (One of the card is face card is selected)
= 2×(40/52)×(12/51)
= 960/2652
= 0.3619
P [X = 2] = P (Two of the 12 card is chosen in the draw)
= (12/52)×(11/51)
= 132/2652
= 0.0498
The variable Y denotes number of cards numbered 10 . Thus, it can take values:
Y = {0, 1, 2 }
P [Y = 0] = P (None of the 4 card is chosen in either draw)
= (48/52)×(47/51)
= 2256/2652
= 0.8507
P [Y = 1] = P (One of the 4 card is chosen in either draw)
= 2×(4/52)×(48/51)
= 384/2652
= 0.1448
P [Y = 2] = P (Two of the 4 card is chosen in the draw)
= (4/52)×(3/51)
= 12/2652
= 0.0045
Now compute the probability of (X and Y).
P [X = 0 and Y = 0] = P(None of the 16 card is chosen in either draw)
= (36/52)×(35/51)
= 1260/2652
= 0.4751
The variables X and Y are independent if,
P [X = 0 and Y = 0] = P [X = 0] × P [Y = 0]
= P [X = 0] × P [Y = 0]
= 0.8507 × 0.5882
= 0.5204
The two values are not equal.
Hence, the variables X and Y are not independent.
I NEED THE ANSWER AS SOON AS POSSIBLE PLEASE!!
Answer:
[tex]\Large \boxed{\sf \ \ 4\sqrt{a^2+b^2} \ \ }[/tex]
Step-by-step explanation:
Hello,
You can use Pythagoras in the 4 right triangles.
For one triangle it comes [tex]\sqrt{a^2+b^2}[/tex].
Then for the polygon it gives [tex]4\cdot \sqrt{a^2+b^2}[/tex].
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Find the volume of the given solid region in the first octant bounded by the plane 9z+15y+15z=45 and the coordinate planes, using triple integrals.
First,
[tex]9x+15y+15z=45\implies 3x+5y+5z=15[/tex]
The volume is given by the integral (one of 6 possible combinations),
[tex]\displaystyle\int_0^5\int_0^{\frac{15-3x}5}\int_0^{\frac{15-3x-5y}5}\mathrm dz\,\mathrm dy\,\mathrm dx=\boxed{\frac{15}2}[/tex]
Please help. I’ll mark you as brainliest if correct! Don’t understand this math problem.
Answer:
work is pictured and shown
Answer:
Infinitely many solutions.
Step-by-step explanation:
To solve the system of equation using the substitution method, the problem has already given us a solution for x:
x = -4y - 9
Using this, we can plug that into the first equation and solve for y:
3x + 12y = -27
3(-4y - 9) + 12y = -27
-12y - 27 + 12y = -27
-27 = -27
The fact that our solution indicate -27 = -27 means that these two equations have infinitely many solutions for the value y. This simply means that no matter what we put in for y, the statement will always be true.
Notice that these two equations are in fact the same equation:
x = -4y - 9 ==> x + 4y = -9 ==> 3x + 12y = -27
Since these two equations are the same, then there are infinitely many solutions.
I'm not sure quite what they want for the form in terms of y, but let's solve for y since they already solved for x:
x = -4y - 9
x + 9 = -4y
y = (-1 / 4) (x + 9)
Cheers.
k/4 + 3= 14 k = pls help
Answer:
k = 44
Step-by-step explanation:
k/4 + 3 = 14
k/4 = 11
k = 44
Answer:
[tex]\boxed{\sf k=44}[/tex]
Step-by-step explanation:
[tex]\sf \frac{k}{4} +3=14[/tex]
Subtract 3 from both sides.
[tex]\sf \frac{k}{4} +3-3=14-3[/tex]
[tex]\sf \frac{k}{4}=11[/tex]
Multiply both sides by 4.
[tex]\sf \frac{k}{4}(4)=11(4)[/tex]
[tex]\sf k=44[/tex]
Two ballpoint pens are selected at random from a box that contains3 blue pens, 2 red pensand 3 green pens. If X is the number of blue pens
Answer: 3/(28) ≈ 10.7%
Step-by-step explanation:
3 blue + 2 red + 3 green = 8 total pens
First pick and Second pick
[tex]\dfrac{3\ blue\ pens}{8\ total\ pens}\quad \times \quad \dfrac{2\ remaining\ blue\ pens}{7\ remaining\ total\ pens}\quad =\large\boxed{\dfrac{3}{28}}[/tex]
Please! help and tell me the answers, or help me figure out these answers for 20 points? please! And please help me. Can anybody help me?
Answer:
1. Pattern (rule) : y = x-6
2. Pattern (rule) : y=x^2+1
3. Pattern (rule) : y = -3x
4. Pattern (rule) : y = 2x-2
5. Pattern (rule) : y = x^2
Step-by-step explanation:
Note: question number correspond to your order of questions.
1. Pattern (rule) : y = x-6
for missing parts, see attached table.
2. Pattern (rule) : y=x^2+1
3. Pattern (rule) : y = -3x
4. Pattern (rule) : y = 2x-2
5. Pattern (rule) : y = x^2
A study regarding the relationship between age and the amount of pressure sales personnel feel in relation to their jobs revealed the following sample information. At the 0.10 significance level, is there a relationship between job pressure and age.
(Round your answers to 3 decimal places.)
Degree of Job Pressure
Age (years) Low Medium High
Less than 25 25 27 20
25 up to 40 49 53 40
40 up to 60 59 59 52
60 and older 35 42 44
H0: Age and pressure are not related. H1: Age and pressure are related.
Reject H0 if X2 > .
X2=
(Click to select)Reject Do not reject H0. Age and pressure (Click to select)areare not related.
Answer:
Reject H0
Age and pressure are related
Step-by-step explanation:
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value. In the given scenario we reject the null hypothesis because job pressure and age are related to each other.
Fifty students are enrolled in a Business Statistics class. After the first examination, a random sample of 5 papers was selected. The grades were 60, 75, 80, 70, and 90. a) Determine the standard error of the mean
Answer:
The standard error S.E of the mean is 5
Step-by-step explanation:
From the given data;
Fifty students are enrolled in a Business Statistics class.
After he first examination, a random sample of 5 papers was selected.
Now; let consider a random sample of 5 papers was selected. with the following grades : 60, 75, 80, 70, and 90
The objective of this question is to determine the standard error of the mean
In order to achieve this ; we need to find the mean and the standard deviation from the given data.
TO start with the mean;
Mean [tex]\overline X[/tex] = [tex]\dfrac{1}{n} \sum x_i[/tex]
Mean [tex]\overline X[/tex] = [tex]\dfrac{1}{5} (60+75+80+70+90)[/tex]
Mean [tex]\overline X[/tex] = 0.2(375)
Mean [tex]\overline X[/tex] = 75
On the other hand; the standard deviation is :
[tex]s = \sqrt{\dfrac{1}{n-1}\sum(x_i - \overline X)^2}[/tex]
[tex]s = \sqrt{\dfrac{1}{5-1}((60-75)^2+(75-75)^2+(80-75)^2+(70-75)^2+(90-75)^2 )}[/tex]
[tex]s = \sqrt{\dfrac{1}{4}(225+0+25+25+225 )}[/tex]
[tex]s = \sqrt{\dfrac{1}{4}(500 )}[/tex]
[tex]s = \sqrt{125}[/tex]
s = 11.18
Finally; the standard error S.E of the mean is:
[tex]S.E = \dfrac{s}{\sqrt{n}}[/tex]
[tex]S.E = \dfrac{11.18}{\sqrt{5}}[/tex]
[tex]S.E = \dfrac{11.18}{2.236}[/tex]
[tex]S.E = 5[/tex]
The standard error S.E of the mean is 5
All sides of the building shown above meet at right angles. If three of the sides measure 2 meters, 7 meters, and 11 meters as shown, then what is the perimeter of the building in meters?
Answer:
69 meters
Step-by-step explanation:
Answer:
Please privately chat to us why you chose to cheat during online class, otherwise we will contact your parents and kick you out of our program for the reason stated.
Step-by-step explanation:
Please contact your Quantitive Reasoning teacher at her email, as stated in Google Classroom.
Edit: I figured it out, it's 14+7(sqrt sign) 2
A square piece of paper is folded once so that one pair of opposite corners coincide. When the paper is unfolded, two congruent triangles have been formed. Given that the area of the original square is $49$ square inches, what is the number of inches in the perimeter of one of these triangles? Express your answer in simplest radical form.
Answer:
[tex]Perimeter = 14 + 7\sqrt{2}[/tex]
Step-by-step explanation:
Given:
Area of the square = 49 in²
Required
Determine the perimeter of the one of the congruent triangles
First, we'll determine the length of the square;
[tex]Area = Length * Length[/tex]
Substitute 49 for Area
[tex]49 = Length * Length[/tex]
[tex]49 = Length^2[/tex]
Take Square root of both sides
[tex]7 = Length[/tex]
[tex]Length = 7[/tex]
When the square is divided into two equal triangles through the diameter;
2 sides of the square remains and the diagonal of the square forms the hypotenuse of the triangle;
Calculating the diagonal, we have;
[tex]Hypotenuse^2 = Length^2 + Length^2[/tex] -- Pythagoras Theorem
[tex]Hypotenuse^2 = 7^2 + 7^2[/tex]
[tex]Hypotenuse^2 = 2(7^2)[/tex]
Take square root of both sides
[tex]Hypotenuse = \sqrt{2} * \sqrt{7^2}[/tex]
[tex]Hypotenuse = \sqrt{2} * 7[/tex]
[tex]Hypotenuse = 7\sqrt{2}[/tex]
The perimeter of one of the triangles is the sum of the 2 Lengths and the Hypotenuse
[tex]Perimeter = Length + Length + Hypotenuse[/tex]
[tex]Perimeter = 7 + 7 + 7\sqrt{2}[/tex]
[tex]Perimeter = 14 + 7\sqrt{2}[/tex]
In the figure below, which term best describes point L?
Explanation:
The tickmarks show which pieces are congruent to one another, which in turn show the segments have been bisected (cut in half). The square angle markers show we have perpendicular segments. So we have three perpendicular bisectors. The perpendicular bisectors intersect at the circumcenter. The circumcenter is the center of the circumcircle. This circle goes through all three vertex points of the triangle.
A useful application is let's say you had 2 friends and you three wanted to pick a location to meet for lunch. Each person traveling from their house to the circumcenter's location will have each person travel the same distance. We say the circumcenter is equidistant from each vertex point of the triangle. In terms of the diagram, LH = LJ = LK.
Answer: B.) Circumcenter
Step-by-step explanation:
Given the equation (x−13)2+y2=64, identify the center and radius. Do not enter any spaces when typing your answers.
Answer:
centre = (13,0)
radius = 8
Step-by-step explanation:
The standard equation of the circle is
(x-x0)^2 + (y-y0)^2 = r^2 ...............(1)
where
(x0,y0) is the centre,
r is the radius.
For
(x-13)^2 + y^2 = 64 ..............(2)
we rewrite (2)
(x-13)^2 + (y-0)^2 = 8^2 ...............(3)
and compare (3) with (1)
to identify
x0 = 13, y0 = 0, and r = 8
Therefore
centre = (13,0)
radius = 8
Which relation is a function?
Answer:
A
Step-by-step explanation:
A function is that of which has only one x value. Therefore you are looking for the graph that does not have multiple x values. Doing a vertical line test to see whether there is more than one point on a line of the graph will show you that A is the only one that has one answer for each x value that is given. All the other graphs have two points for some of the x's, which makes them not a function.
please I need help with this question!
The weight of adult males in Boston are normally distributed with mean 69 kilograms and variance 25 kilograms.
I. what percentage of adult male in Boston weigh more than 72 kilograms?
ii. what must an adult male weigh in order to be among the heaviest 10% of the population?
Thank you in advance!
Answer:
lmkjhvjgcfnhjkhbmgnc gfghh
Step-by-step explanation:
Which of the following inequalities is not true?
A) -2/2 < 3
B) |-1| ≥ 0
C) |-9| ≠ |9|
D) -7 ≤ -5
Answer:
C) |-9| != |9|
Step-by-step explanation:
The definition of absolute value is simply the non-negative value of the argument without regards to the sign. With this in mind, let's walk through these options.
A) -2/2 < 3 ==> -1 < 3 which is True
B) |-1| >= 0 ==> 1 >= 0 which is True since 1 is > 0
C) |-9| != |9| ==> 9 != 9 which is False since 9 == 9
D) -7 <= -5 which is True since -7 is < -5
Cheers
These two polygons are similar.
Answer:
[tex]\huge\boxed{z=3}[/tex]
Step-by-step explanation:
If two polygons are similar, then corresponding sides are in proportion.
The corresponding sides:
4 → x
y → 15
3 → w
2 → 6
z → 9
therefore:
[tex]\dfrac{z}{9}=\dfrac{2}{6}[/tex] cross multiply
[tex](z)(6)=(9)(2)[/tex]
[tex]6z=18[/tex] divide both sides by 6
[tex]z=3[/tex]
Answer:
Step-by-step explanation:
The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume there are 360 days in a year. P = $7000, r = 0.2%, t = 6months
Answer:
$7
Step-by-step explanation:
Simple interest formula:
I = Prt
6 months = 6 * 30 days = 180 days
1 year = 360 days
t = (180 days)/(360 days) = 0.5
I = $7000 * 0.002 * 0.5
I = $7
Answer:
$7
Step-by-step explanation:
Recall that simple interest is given by
I = Prt,
Where :
I = interest (we are asked to find this)
P = principal amount = given as $7000
r = rate = given as 0.2% = 0.002
t = time in years = given as 6 months = 0.5 years
SImply substitute the known values into the equation above:
I = Prt
= (7000)(0.002)(0.5)
= $7