Answer:
t=44°
Step-by-step explanation:
The sum of the interior angles of any pentagon is always 540 degrees.
Let's set up an equation with this information: (all figures are in degrees)
[tex]t+3t+t+32+149+139=540[/tex]
Now we combine all like terms.
[tex]5t+320=540[/tex]
Now begin to isolate t be subtracting 320 from both sides.
[tex]5t=220[/tex]
Finally divide both sides by 5 to isolate t.
t=44°
Variables and Inequalities
Answer:
28 - 7x =< 28x + 28
28 - 35x =< 28
-35x =< 0
x >= 0
the answer is the fourth one
x is greater than or equal to 0
At what time the sum Rs. 5000 will be doubled at the interest
of 10% per annum?
Answer:
Time= [tex]10[/tex] years
Step-by-step explanation:
Let total time[tex]=t[/tex]
Initial Amount[tex]=5000[/tex]
Final Amount[tex]=10000[/tex]
Total interest = Final Amount - Initial Amount
[tex]=10000-5000\\=5000[/tex]
Simple Interest [tex]=\frac{Initial Amount\times time\times rate}{100} \\\\5000=\frac{5000\times t \times 10}{100}\\\frac{t}{10} =1\\t=10 \ years[/tex]
find the value of 2x-yi fx+y=8and4x-y=22
Answer:
10
Step-by-step explanation:
Given
[tex]x+y=8\\ \\4x-y=22[/tex]
Add these two equations:
[tex]x+y+4x-y=8+22\\ \\5x=30\\ \\x=6[/tex]
Substitute it into the first equation:
[tex]6+y=8\\ \\y=8-6\\ \\y=2[/tex]
Then
[tex]2x-y=2\cdot 6-2=12-2=10[/tex]
Mr.Garison purchases a new freezer. Before he can store food in it, the freezer is 21C. If the temperature in the freezer decreases at a rate of 3 per hour, how long will it take the freezer to reach -18C?
Answer:13hrs
Step-by-step explanation:
Initial Temperature = 21°c
final temperature = -18°c
rate of decrease = 3°c/hr
for every hour the temperature decreases by 3°c.
What time does it take to get to 0c = . 21(°c) / 3(°c/hr) = . 7hr
what time does it take to get to -18c = 18(°c) / 3(°c/hr) = . 6hr
Total Time taken = . 7hr + 6hr = 13hr
Alternative solution
Initial Temperature = 21°c
final temperature = -18°c
rate of decrease = 3°c/hr
(21 + 18)°c/ 3(°c/hr) . = . 13hr
To cool a freezer from 21℃ to -18℃ at a rate of 3℃ per hour, it would take 13 hours for the freezer to reach -18℃.
The question asks how long it will take for a freezer to cool down from 21℃ to -18℃ if the temperature decreases at a rate of 3℃ per hour. To find the time it takes, you'll need to calculate the total temperature change required and then divide by the rate of temperature change.
First, calculate the total temperature difference:
21℃ (starting temperature) - (-18℃ target temperature) = 39℃ total temperature change.
Next, divide the total temperature change by the rate of temperature change:
39℃ total change / 3℃ per hour = 13 hours required
for the freezer to cool from 21℃ to -18℃.
Box A holds about
50 marbles. Box B
could hold about
O 5 marbles
O 150 marbles
075 marbles
Answer:
Lack of information.
Step-by-step explanation:
We can't get the answer because this question haven't provide the information enough.
Have a nice day and hope it helps ;)
Pedro invests £800 in a bank account that pays 3% simple interest per year. How much money will he have in his account after 3 years?
874.18
Step-by-step explanation:if you multiply 800 by1.03 it will increase by 3% then repeat step two more times
7. Determine if the set of ordered pairs is a relation or a function. Select all that apply.
{(2, 2), (3, 2), (4, 3), (5,4)}
The given relation is a function
Step-by-step explanation:
When a relation is given in the form of ordered pairs, for each ordered pair, the first element of ordered pair represents elements of domain and the second element represents elements of set of range.
In order for a relation to be a function, there should be no repetition in domain i.e. every element should be unique.
Given relation is:
{(2, 2), (3, 2), (4, 3), (5,4)}
As we can see that the domain of given relation is:
{2,3,4,5} i.e. every element is unique
So,
The given relation is a function
Keywords: Relations, functions
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The provided set of ordered pairs {(2, 2), (3, 2), (4, 3), (5,4)} represents both a relation and a function. This holds because each input maps to exactly one output, with no repeating input values.
Explanation:In mathematics, a set of ordered pairs is a relation if input values (also known as the domain or x-values) may have any number of corresponding output values (the range or y-values). A set of ordered pairs is a function if each input value maps to exactly one output value.
Considering the set of ordered pairs: {(2, 2), (3, 2), (4, 3), (5,4)}, we can see that each input (x-value) matches with one corresponding output (y-value) and none of the input values is repeating. Hence, according to the definition, this set of ordered pairs represents both a relation and a function.
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The temperature in Fairbanks, Alasks rose from negative one degrees Fahrenheit to nine degrees Fahrenheit. How many degrees did the temperature change?
Answer:
There was 10° F change in temperature in Fairbanks, Alaska.
Step-by-step explanation:
Given:
Temperature change from = -1° F.
Temperature change to = 9° F
We need to find the change in temperature.
Change in temperature can be calculated by subtracting Temperature change from with Temperature change to.
Framing in equation form we get;
Change in temperature = Temperature change to - Temperature change from
Substituting the values we get;
Change in temperature = [tex]9-(-1)= 9+1=10\° F[/tex]
Hence There was 10° F change in temperature in Fairbanks, Alaska.
Use the estimation to check weather 128is a reasonable answer in the example above p=200-72
Answer:
130 is close to 128, so 128 is a reasonable answer.
Step-by-step explanation:
Consider the provided information.
We need to Use the estimation to check weather 128 is a reasonable answer in the example above:
p=200-72
Round to the nearest ten: p = 200 - 70
Subtract the rounded numbers: 200-70=130
130 is close to 128, so 128 is a reasonable answer.
What is an equation of a line that passes through the points (8 , -3) (8 , 4)
Answer:
Step-by-step explanation:
(8,-3),(8,4)
since both points have the same x value, this means you have a vertical line with an undefined slope...so ur equation would be x = 8....because no matter what y is, x will always be 8
What is the product of x(5x + x^2)
Answer:
The product is [tex]x^3+5x^2[/tex]
Step-by-step explanation:
This is because we apply the distributive property of multiplication.
Thus from [tex]x(5x+x^2)[/tex]
we get this:
[tex]x*5x+x*x^2[/tex]
[tex]x*5x[/tex] is [tex]5x^2[/tex] and [tex]x*x^2[/tex] is [tex]x^3[/tex]
Information about how the students at Vista View High School got to school this morning is shown in the table. A 6-column table has 4 rows. The first column has entries Tenth grade, eleventh grade, twelfth grade, Total. The second column is labeled Walk with entries 104, blank, 99, 314. The third column is labeled Bicycle with entries 8, 10, blank, blank. The fourth column is labeled Bus with entries 96, 72, 28, 196. The fifth column is labeled Car with entries blank, 88, blank, 276. The sixth column is labeled Total with entries 282, blank, 252, 815. Out of all 252 twelfth graders, how many rode in a car to school? 11 74 111 114
Answer:
The correct answer is D. 114
Step-by-step explanation:
There are 252 students of twelfth grade at Vista View High School.
99 walked to school
11 went by bicycle
28 used the school bus
To find the amount of twelfth graders that rode in a car, we do this calculation:
Amount of twelfth graders that rode in a car = Total of twelfth graders - those who walked - those who went by bicycle - those who used the bus
Replacing with the real values, we have:
Amount of twelfth graders that rode in a car = 252 - 99 - 11 - 28 = 252 - 138 = 114
The correct answer is D. 114
Answer:
114
Step-by-step explanation:
The triangle shown is classified as
acute, isosceles
right, isosceles
obtuse, isosceles
right, equilateral
Answer:
b. Right, isosceles
Step-by-step explanation:
right because it has a right angle at the top corner
isosceles because two sides of the triangle are equal to each others
Find the y intercept (-3,19) and (6,13)
Answer:
Step-by-step explanation:
We will first find the slope of the line from those 2 points, then write the equation of the line in slope-intercept form, solving for b, the y-intercept.
[tex]m=\frac{13-19}{6-(-3)}=-\frac{6}{9}=-\frac{2}{3}[/tex]
So the slope is -2/3. We will choose a point now to use in the slope-intercept equation. I'm picking the one with no negatives (cuz who likes negatives!?).
[tex]13=-\frac{2}{3}(6)+b[/tex] which simplifies down to
13 = -4 + b so
b = 17
The y-intercept of the line that goes through those 2 points is (0, 17)
2.
The average monthly rent for a one-bedroom home in San Francisco is $1229. A random
sample of 15 one-bedroom homes outside the city had a mean rent of $1350. At a = 0.05,
can we conclude that the rent outside the city differs from the rent in the city?
Answer
given,
average rent of one bed room = $1229
sample size = n = 15
Sample mean rent = $1350
Assuming standard deviation equal to $250
the test hypothesis is
H o: µ=1229
H a: µ not equal to 1229
now we know,
[tex]t = \dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \dfrac{\$ 1350-\$ 1229}{\dfrac{250}{\sqrt{15}}}[/tex]
t = 1.875
from t- table
a=0.05, the critical value is |t(0.025, d f= n-1 = 14)|=2.14
since t= 1.875 which is less than 2.14 we do not reject H o.
So we can not conclude that the monthly rent outside San Francisco differs from that in the city
At a 0.05 significance level, we cannot conclude that the monthly rent outside San Francisco differs from that in the city, based on the given data and hypothesis test.
To determine if the monthly rent outside San Francisco differs from that in the city based on the sample provided, we perform a hypothesis test. Our null hypothesis (H0) states that the mean rent outside San Francisco is equal to the average rent in San Francisco, i.e., $1229. The alternative hypothesis (Ha) posits that the mean rent outside San Francisco is different from $1229.
Calculate the test statistic: We use a Z-test since the population standard deviation is known. The formula for the Z-score is:
[tex]Z = \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
where X_bar = 1350, μ = 1229, σ = 250, and n = 15. Plugging in these values:
[tex]Z = \frac{1350 - 1229}{\frac{250}{\sqrt{15}}} = \frac{121}{64.55} \approx 1.87[/tex]
Determine the critical value: At α = 0.05, the critical values for a two-tailed test are approximately ±1.96.
Compare the test statistic to the critical value: Since 1.87 is less than 1.96, we fail to reject the null hypothesis.
Conclusively, at the 0.05 significance level, we do not have enough evidence to say that the monthly rent outside San Francisco differs from that in the city.
Complete question:
The average monthly rent for a one-bedroom home in San Francisco is $1229. A random sample of 15 one-bedroom homes about 15 miles outside of San Francisco had a mean rent of $1350. The population standard deviation is $250. At α = 0.05, can we conclude that the monthly rent outside San Francisco differs from that in the city?
Romeo paid $380.75 in car repairs. The sales Tax rate is 7.5% . Which of the following is a responsible estimate for the total Romeo paid to repair his car?
A $28.50
B $410.00
C $352.50
D $442.00
Answer:A
Step-by-step explanation:
no need for this you only look at the answers
Using mathematical language, explain how you know there will be one solution to the system shown. Tortoise: f = 2m + 180, Hare: f = 8m
Answer:
30
Step-by-step explanation:
2m+180=8m
180=8m-2m
180=6m
m=180/6
m=30
Because the two lines are not parallel, we conclude that the system will have a solution.
How do we know that the system will have a solution?
Remember that the solution of a system of equations is the point where the graphs of the functions intersect.
In this case we have two linear functions:
f = 2m + 180
f = 8m
Notice that the slopes are different, this means that the lines are not parallel, and because of that, we know that the lines will intersect at some point. That is enough to know that the system has a solution.
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The length of a rectangle is three times the width. The perimeter of the rectangle is 32 inches. What is the area of the rectangle (in square inches)?
To find the area of this rectangle, we first solve for the width using the given perimeter, yielding 4 inches. The length, three times this, is 12 inches. Multiplying these values together gives an area of 48 square inches.
Explanation:We are dealing with a rectangle whose length is three times its width. If we call the width of the rectangle 'w', then its length is '3w'. The perimeter of a rectangle is 2 times the sum of its length and width.
So 2*(w+3w) = 32. This simplifies to 8w = 32. Solving for 'w', we find that the width of the rectangle is 4 inches. Then, the length would be three times the width, which is 12 inches.
Having determined these dimensions, we can find the area of the rectangle. The area of a rectangle is its length multiplied by its width. So in this case, it would be 4 inches (width) times 12 inches (length) to give us an area of 48 square inches.
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Find the value of 3u-8 given that -7u + 9=2
Answer:
-5
Step-by-step explanation:
-7u+9=2
-7u=2-9
-7u=-7
7u=7
u=7/7
u=1
3(1)-8=3-8=-5
What is the distance, in feet, across the patch of swamp water?
Answer:
Therefore the distance across the patch of swamp water is 50 ft
Step-by-step explanation:
Given:
VW = 100 ft
WX = 60 ft
XZ = 30 ft
To Find:
ZY = l = ?
Solution:
In Δ VWX and Δ YZX
∠W ≅ ∠ Z …………..{measure of each angle is 90° given}
∠VXW ≅ ∠YXZ ..............{vertically opposite angles are equal}
Δ ABC ~ Δ DEC ….{Angle-Angle Similarity test}
If two triangles are similar then their sides are in proportion.
[tex]\frac{VW}{YZ} =\frac{WX}{ZX} =\frac{VX}{YX}\ \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
On substituting the given values we get
[tex]\frac{100}{l} =\frac{60}{30}\\\\l=\frac{3000}{60}=50\ ft[/tex]
Therefore the distance across the patch of swamp water is 50 ft
Solve the given equation.
-6. 15*+5 = -75
Answer: -30.75=-75
Step-by-step explanation: Multiply -6.15 by 5.
Hope this helps you out.
If the domain of the function F = {(x, y) |2x + y = 7} is {1, 2, 3), what is the range?
O {1,2,3}
O (1,3,5)
O {2,5/2, 3)
Answer:
1,3,5
Step-by-step explanation:
The domain is the set of all first elements of ordered pairs (x-coordinates).
The range is the set of all second elements of ordered pairs (y-coordinates).
Answer:
Step-by-step explanation:
y = 7 - 2x
x =1; y = 7 - 2*1 = 7- 2 = 5
x = 2; y = 7 - 2*2 = 7 - 4 = 3
x = 3; y = 7 - 2*3 = 7- 6 = 1
Range = { 1,3,5}
what is the result of subtracting the second equation from the first? x-3y=6 -8x-y=6 (picture included if confusing) please help!! :(
This is the new equation obtained after performing the subtraction.
[tex]\[ 9x - 2y = 0 \][/tex]
When subtracting one equation from another, we subtract the corresponding elements of the equations. Here's the step-by-step process:
Given the two equations:
1. [tex]\( x - 3y = 6 \)[/tex] (First equation)
2. [tex]\( -8x - y = 6 \)[/tex] (Second equation)
We want to subtract the second equation from the first. We do this by subtracting each term of the second equation from the corresponding term in the first equation:
Step 1: Subtract the x-terms:
[tex]\[ x - (-8x) = x + 8x = 9x \][/tex]
Step 2: Subtract the y-terms:
[tex]\[ -3y - (-y) = -3y + y = -2y \][/tex]
Step 3: Subtract the constants:
[tex]\[ 6 - 6 = 0 \][/tex]
So after subtracting the second equation from the first, the result is:
[tex]\[ 9x - 2y = 0 \][/tex]
This is the new equation obtained after performing the subtraction.
mathematics help plz
Answer:
Below.
Step-by-step explanation:
-1 + r ≥ 4
Add 1 to both sides:
r ≥ 5.
The graph will have a filled circle on the number 5 and a heavy line to the right.
Given: Rays I and M are bisectors of the angels of triangle ABC . X is the intersection of ray’s I and M, line XD is perpendicular to line AC , line XE is perpendicular to line AB, and line XF is perpendicular to line BC. Prove love XD equals line XE ands is also equal to XF
A. ASA
B. AAS
C. SAS
D. SSS
Line XD equals line XE and is also equal to line XF that proved by using AAS postulate of congruence ⇒ B
Step-by-step explanation:
Let us revise the cases of congruence
SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ HL ⇒ hypotenuse leg of the 1st right Δ ≅ hypotenuse leg of the 2nd right ΔIn Δ ABC
∵ Ray AL bisects ∠A ⇒ (divides it into two equal angles)
∴ m∠DAX = m∠EAX
∵ Ray BM bisects ∠B ⇒ (divides it into two equal angles)
∴ m∠EBX = m∠FBX
∵ XD ⊥ AC
∴ m∠XDA = 90°
∵ XE ⊥ AB
∴ m∠XEA = 90°
∵ XE ⊥ BC
∴ m∠XFB = 90°
Now lets prove that Δ ADX and ΔAEX are congruent
In Δs ADX and AEX
∵ m∠ADX = m∠AEX ⇒ (their measures are 90°)
∵ m∠DAX = m∠EAX ⇒ proved
∵ AX is a common side in both triangles
- By using the AAS postulate of congruence
∴ Δ ADX ≅ Δ AEX
∴ XD = XE
Let us do the same with Δ BEX and Δ BFX
In Δs BEX and BFX
∵ m∠BEX = m∠BFX ⇒ (their measures are 90°)
∵ m∠EBX = m∠FBX ⇒ proved
∵ BX is a common side in both triangles
- By using the AAS postulate of congruence
∴ Δ BEX ≅ Δ BFX
∴ XE = XF
∵ XE = XD
∵ XE = XF
- If one side is equal two other sides then the two other sides are
equal, that means the three sides are equal
∴ XD = XF
∴ XD = XE = XF
Line XD equals line XE and is also equal to line XF that proved by using AAS postulate of congruence
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in a program designed to help patients stop smoking 232 patients were given sustained care and 84.9% of them were no longer smoking after one month use a 0.05 significance level to test the claim that 80% of the patients. Smoking when given sustained care
Answer:
[tex]z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869[/tex]
[tex]p_v =2*P(Z>1.869)=0.0616[/tex]
If we compare the p value obtained and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults were no longer smoking after one month is not significantly different from 0.8 or 80% .
Step-by-step explanation:
1) Data given and notation
n=232 represent the random sample taken
X represent the adults were no longer smoking after one month
[tex]\hat p=0.849[/tex] estimated proportion of adults were no longer smoking after one month
[tex]p_o=0.80[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is 0.8.:
Null hypothesis:[tex]p=0.8[/tex]
Alternative hypothesis:[tex]p \neq 0.8[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869[/tex]
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(Z>1.869)=0.0616[/tex]
If we compare the p value obtained and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults were no longer smoking after one month is not significantly different from 0.8 or 80% .
How many times can 4 go into 75
Answer:
solve using long division.
75/4
what is the largest whole number smaller than 75 that 4 can go into?
72.
how many times can 4 go into 72?
18.
so then subtract 72 from 75 to get 3.
the new equation is
3/4
how many times can 3 go into 4?
0.75 times.
so add the 2 answers to get
18.75
4 can go into 75 18.75 times.
To determine how many times 4 can go into 75, you divide 75 by 4. The result is 18 with a remainder of 3. Thus, 4 can go into 75 a total of 18 full times.
To find out how many times 4 can go into 75, we need to perform a division. Specifically, we need to divide 75 by 4.
Divide: 75 ÷ 4 = 18 with a remainder.Multiply: 4 × 18 = 72.Subtract: 75 - 72 = 3.This means that 4 goes into 75 exactly 18 times with a remainder of 3. So, 4 fully fits into 75 for 18 full times.
Tim and Tom are trying to earn money to buy a new game system over a 3-month period. Tim saved $45.19 each month. If they need a total of $211.29 to buy the game system, how much does Tom need to earn each of the 3 months in order to buy the game system?
Answer:
$25.24
Step-by-step explanation:
If Tim earns $45.19 each month multiply by 3 which gives you $135.57 take $211.29 subtract $135.57, you get $75.72 which is the total amount that Tom needs to give. Divide that by 3 and get $25.64 which is the amount Tom needs in 3 months.
$45.19 x 3 = $135.57
$211.29 - $135.57 = $75.72
$75.72/3 = $25.24
-1/3h-2/3=1/7 Do you know the answer?
Answer:
-51/21
The first step in this equation would be to add -2/3 to 1/7
-2/3 and 1/7 need to have the same denominator, which 7 and 3 both go into 21
-2/3 converted to have the denominator, you would have to times top and bottom by 7, so you then get 14/21
Then you want to get the 1/7 with a denominator of 21 also, so you would times top and bottom by 3, so you get 3/21
Now you add 14/21 to 3/21 to get 17/21
-1/3h=17/21
You want to times by the reciprocal of -1/3 which would just be -3/1 so,
17/21*-3/1= -51/21 which is already simplified
So your answer would be -51/21
To check your work you would plug in -51/21 in for h
Step-by-step explanation:
Which expression is equivalent to
5-4/4-3
Answer:
1
Step-by-step explanation:
4/4=1
5-1-3=4-3=1