Based on the required width and height of the tent, the length of the cloth would have to be 14.4 ft.
How long should the length of the cloth be?The opening of the tent would be an isosceles triangle but if it is divided in two from the top, a right-angled triangle will be formed and the hypotenuse will be the length of the cloth on one side.
That length - according to the Pythagoras theorem - would be:
= √(6² + (8 /2)²)
= √(36 + 16)
= 7.2 ft
As this is the length of one side of the cloth, the length of the entire cloth is:
= 7.2 x 2
= 14.4 ft
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What is the solution to the equation below? Round your answer to two
decimal places.
log2(2x-1) = 3
A. x=4
O B. x= 1/2
732
O c. x = 2/
O D. x = 5
Answer:
D. x=5
The answer is x=4.50 then it is rounded off to 5. So, the answer is 5.
Step-by-step explanation:
Find the domain of the inequality:[tex]2x-1\geq 0[/tex]
Rearrange terms to the left side of the equation:[tex]2x\geq 1[/tex]
Divide both sides of the inequality by the coefficient of the variable:
=> [tex]x\geq \frac{1}{2}[/tex]
The domain of the inequality is:[tex]x\geq \frac{1}{2}[/tex]
Convert logarithm to exponential form:[tex]2^{3}=2x-1[/tex]
Calculate the power:[tex]8=2x-1[/tex]
Rearrange terms to the left side of the equation:[tex]-2x= -8-1[/tex]
Calculate:[tex]-2x=-9[/tex]
Divide both sides of the equation by the coefficient of the variable:[tex]x=\frac{-9}{-2}[/tex]
=> [tex]x=\frac{9}{2}[/tex]
=>[tex]x=4.5\\[/tex]
Round the number: [tex]x=4.50[/tex]
Answer: [tex]x=4.50[/tex]
=> [tex]x=5[/tex]
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Answer:
x = 9/2
Step-by-step explanation:
3.14(a2 + ab) when a = 4 and b = 3
Step-by-step explanation:
how does the picture fit into this question ?
I guess you mean
(a² + ab)
when a = 4 and b = 3. then we simply replace the variable names by the actual values and calculate :
4² + 4×3 = 16 + 12 = 28
.
now to the picture :
i am not sure what the requested result of procedure is.
so, I am just going to simplify the expression :
(log(25) - log(4)) / (log(55) - 1/2 × log(2)
remember the rules of the logarithm :
log(a) - log(b) = log(a/b)
k × log(a) = log(a^k)
a^(1/2) = sqrt(a) (the square root of a)
I assume we are using the logarithm to the base of 10.
so, we have here
log(25/4) / log(55/sqrt(2)) =
= 0.795880017... / 1.589847692... = 0.500601423...
What's x ? find the indicated side of the right triangle
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{x = 6}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{The image provided with 2 angles and one side}[/tex]
Find: [tex]\textsf{Solve for the unknown side of x}[/tex]
Solution: In order to determine the length of x we need to use some trigonometric functions. Using Soh Cah Toa we can see that we can either use 30 degrees or 60 degrees. We will stick to 60 and we can see that the opposite side is 3 and the hypotenuse is x meaning that we need to use sin. Plug in the values and solve for the unknown.
Plug in the values
[tex]\textsf{sin(30) = }\frac{\textsf{opposite}}{\textsf{hypotenuse}}[/tex][tex]\textsf{sin(30) = }\frac{\textsf{3}}{\textsf{x}}[/tex]Multiply both sides by x
[tex]\textsf{sin(30) * x = }\frac{\textsf{3}}{\textsf{x}}\textsf{ * x}[/tex][tex]\textsf{sin(30) * x = 3}[/tex]Divide both sides by sin(30)
[tex]\textsf{sin(30) * x}*\frac{1}{\textsf{sin(30)}}\textsf{ = 3}}*\frac{1}{\textsf{sin(30)}}[/tex][tex]\textsf{x = 3}}*\frac{1}{\textsf{sin(30)}}[/tex]Simplify
[tex]\textsf{x = 3}}*\frac{1}{\textsf{0.5}}[/tex][tex]\textsf{x = 6}[/tex]Therefore, the value of the unknown variable x is 6 units.
A 6-sided number cube is rolled twice. What is the probability of getting a 3 on the first roll and a 4 on the second roll? 2.8% 16.7% 20% 33.3%
Answer: 2.8%
Step-by-step explanation:
On the first roll, probability to get a 3 is 1/6.
On the second roll probability to get a 4 is also 1/6.
To get both of these numbers together, you need to multiply the two probabilities.
1/6 x 1/6 = 1/36.
1/36 = ~2.8
2.8%
Answer: 2.8%
Step-by-step explanation: I got it right on the test.
given the formula p=k*2 w, find the value of p if k= 5 and w= - 3
Answer:
-75Step-by-step explanation:
Given:
k= 5w= -3Find: p
Formula: p=k²w
Solution:
p=k2w
➡️ p= (5)²(-3)
➡️ p= 25(-3)
➡️ p= -75
Answer:
p= -75Hope it helps
Compute the projection of u on v.
Answer:
[tex]\frac{3}{7}.v[/tex] option (C) is correct
Step-by-step explanation:
projection of vectors: The vector projection of one vector over another vector is the length of the shadow of the given vector over another vector.
projection of vector u on v is given by :
[tex](\frac{u.v}{v.v}).v[/tex]Given,
vector u = <5, 7, 1>
vector v = <2, -1, 3>
substituting these values in the above formula
[tex][\frac{(2,-1,3)(5,7,1)}{(2,-1,3).(2,-1,3)} ].v[/tex] = [tex]\frac{6}{14}.v= \frac{3}{7}.v[/tex]thus the correct answer is option (C)
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The diameter of a bicycle wheel is 63 cm. How much distance will it cover in 20revolutions?
Answer:
1256 cm
Step-by-step explanation:
First we must find the perimeter, because the perimeter is equal to 1 revolution.
The perimeter of any circle is Pi(Diameter)
3.14*20
62.8 cm is the perimeter of the bike wheel.
Because the perimeter is basically a revolution, we can multiply 62.8 by 20 to get:
1256 cm
the length of a cll is 2/3 mm. if the area of the cell is 1/12 square mm, what is the width of the cell
The width of a cell with the length (l) of the cell is [tex]\frac{2}{3}[/tex] mm and area (A) of the cell is [tex]\frac{1}{12}[/tex] mm² is [tex]\frac{1}{8}[/tex].
Given that, the length (l) of the cell is [tex]\frac{2}{3}[/tex] mm and area (A) of the cell is [tex]\frac{1}{12}[/tex] mm².
We need to find the width of the cell.
What is the area of a rectangle?The area of a rectangle is the product of its length and width. So, the area of the rectangle = Length×Width square units.
Now, the area of a cell = [tex]\frac{2}{3}[/tex] ×Width= [tex]\frac{1}{2}[/tex] mm².
⇒Width=[tex]\frac{\frac{1}{12} }{\frac{2}{3} } ={\frac{1}{12} \times {\frac{3}{2}=\frac{1}{8}[/tex]
Therefore, the width of a cell with the length (l) of the cell is [tex]\frac{2}{3}[/tex] mm and area (A) of the cell is [tex]\frac{1}{12}[/tex] mm² is [tex]\frac{1}{8}[/tex].
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A media personality argues that global temperatures are not rising, because every year an increase is reported, such as 0.09 degrees C. The difference from the previous year is less than the margin of error of about 0.13 degrees C, so that difference should be ignored. What is the best counterargument?
The difference is only 0.04, but that is still a significant change.
The margin of error is quite small compared to the change year over year, so it is a significant issue.
The change of 0.09 is not a lot and thus should be ignored.
The margin of error is larger than the increase, so we should consider it an issue of just extra information and thus can be ignored.
The best counterargument: the margin of error is quite small compared to the change year over year, so it is a significant issue.
What is Margin error?In statistics, the margin of error refers to half the confidence interval. It measures how much of a random sample does not fall within the confidence interval as the number of samples taken increases indefinitely.
As, the temperature rises by 0.09 degree.
So, the difference between margin error and increase is higher which is
= 0.13- 0.09
=0.04
Hence, The margin of error is quite small compared to the change year over year, so it is a significant issue.
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Write an explicit rule to represent the sequence:
20, 24, 28, 32, 36,...
a) f(n)=4n+20
b) f(n)=4n+16
c) f(n)=4n+24
d) f(n)=4n+12
Answer:
b)f(n)=4n+16
Step-by-step explanation:
if n=1
substitute 1 for n in the equation
f(1)=4(1)+16
=4+16
=20
f(2)=4(2)+16
=8+16
=24
And so on
These expressions represent four numbers. The value of the median of the expressions is 12.
Answer:
Try retyping ,which expressions ..?? Maybe it didn't come out
Answer:
15
Step-by-step explanation:
Actual Question:
These expressions represent four numbers. The value of the median of the expressions is 12.
x , 2x, 6x, 11x
Work out the value of the mean of the expressions.
_____________________________________________
See the attachment for steps.
Which expression is the simplest form of - (4x³ + x²) + 2 (x³ − 3x²)?
OA. -2³ - 7x²
OB.
B. -2x³-5x2
O C.-6x³ - 2x²
OD. -6x³6x²
The expression which is the simplest form of; - (4x³ + x²) + 2 (x³ − 3x²) is; -2x³ -7x².
What is the simplest form of the expression?The expression given in the task content whose simplest form is to be determined is;
- (4x³ + x²) + 2 (x³ − 3x²)
Hence, upon opening up the parentheses, it follows that;
-4x³ - x² +2x³ -6x²
Upon collection and summing up of like terms; -2x³ -7x².
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determining height from a shadow measuring 88 meter
Answer:
Height = 132 mt
Step-by-step explanation:
Shadow lengths are proportional to the height of the object.
So, multiply the length of the tree's shadow by your height.
If you are 5 feet (1.5 meters) tall, and the length of shadow is 88 meters long,
Multiply them together: 1.5 x 88 = 132 mt.
Hence, Height = 132 mt.
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URGENT + 20 Points! The regression equation for water being poured into a large, cone-shaped cistern is In(volume) = -1.327 +2.993 In(Time). What is the predicted volume for a time of 12 seconds?
- There is a line above "(volume)"
1.810 cm3
6.110 cm3
34.589 cm3
450.485 cm3
The predicted volume for a time of 12 seconds of the large, cone-shaped cistern is; V = 450.485 cm³
How to Solve Regression Equations?We are given the regression equation;
In V = -1.327 + 2.993 In T
Where;
V is volume
T is time
At T = 12, we have;
In V = -1.327 + 2.993 In 12
In V = -1.327 + 7.4373
In V = 6.1103
V = e^(6.1103)
V = 450.485 cm³
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a cuboid has length 18.5 cm, width 9.4 cm a height 6.2 cm. Work out the area of the cuboid
Answer:
693.76 cm²Step-by-step explanation:
a cuboid has length 18.5 cm, width 9.4 cm a height 6.2 cm. Work out the area of the cuboid
assuming you are looking for thr surface area
Surface Area of a Cuboid ·
TSA = 2 (lw + wh + hl)
2*( 18.5 * 9.4 + 9.4 * 6.2 + 6.2 * 18.5) = (remember PEMDAS)
2 * 346.88 =
693.76 cm²
24. This week, Cristina eamed P594.65 from selling burgers for 35 days. How much he will earn in 5 days?
A. P84.95
B. P94.95
C. P104.95
D. P114.95
25. You have four quizzes in your math subject in a quarter. You got 88.75 for the first quiz, 85.5, 90.5, and 87.25 in the second, third and fourth quizzes, respectively. What is your average in the four quizzes this quarter?
A. 86.5
B. 88
C. 89.5
D. 90 26. Amberich put P580.00 into a savings account for one year. The rate of interest on the account was 6.5%. How much was the interest for one year in pesos and centavos?
A. P67.70
B. P37.70
C. P57.70
D. P17.70
24. This week , Cristina eamed P594.65 from selling burgers for 35 days . How much he will earn in 5 days ?
A. P84.95
B. P94.95
C. P104.95
D. P114.95
25. You have four quizzes in your math subject in a quarter . You got 88.75 for the first quiz , 85.5 , 90.5 , and 87.25 in the second , third and fourth quizzes , respectively . What is your average in the four quizzes this quarter ?
A. 86.5
B. 88
C. 89.5
D. 90
26. Amberich put P580.00 into a savings account for one year . The rate of interest on the account was 6.5 % . How much was the interest for one year in pesos and centavos ?
A. P67.70
B. P37.70
C. P57.70
D. P17.70
Question 24 :
P594.65 : 35 days
P594.65/7 : 35/7 days
P84.95 : 5 days
⇒ A. P84.95
Question 25 :
88.75 + 85.5 + 90.5 + 87.25 / 4
352/4
88
⇒ B. 88
Question 26 :
I = P × r × t
I = 580.00 × 0.065 × 1
I = P37.70
⇒ B. P37.70
Find equation in slope intercept form of the line passing through the points with given coordinates (-4,-2), (-2,2)
Answer:
y = 2x + 6
Step-by-step explanation:
We are given that a line runs through the points (-4,-2) and (-2,2).
We want to write the equation of this line in slope-intercept form.
Slope-intercept form is written as y=mx+b, where m is the slope and b is the value of y at the y intercept, hence the name.
First, we need to find the slope of the line.
The slope can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.
Even though we have two points, let's label the values of the points to avoid confusion & mistakes.
[tex]x_1=-4\\y_1=-2\\x_2=-2\\y_2=2[/tex]
Now let's find the slope (remember: the formula has subtraction):
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{2--2}{-2--4}[/tex]
This can be simplified:
m=[tex]\frac{2+2}{-2+4}[/tex]
Add the numbers together.
m=[tex]\frac{4}{2}[/tex]
Divide.
m = 2
The slope of the line is 2.
We can substitute this into the equation for m.
Here is the equation of the line so far:
y = 2x + b
We now need to find b.
As the equation passes through both (-4, -2) and (-2, 2), we can use either one of them to help solve for b.
Taking (-4, -2) for instance:
Substitute -4 as x and -2 as y in the equation we have.
-2 = 2(-4) + b
Multiply.
-2 = -8 + b
Add 8 to both sides.
6 = b
Substitute 6 as b into the equation.
y = 2x + 6
Topic: finding the equation of the line (slope-intercept form)
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Plss helppppppppppppppp
Answer: [tex]-\frac{3}{2} \leq x < 5[/tex]
Step-by-step explanation:
We can split this into two inequalities, namely [tex]2x-3 < x+2[/tex] and [tex]x+2 \leq 3x+5[/tex].
Solving the first inequality,
[tex]2x-3 < x+2\\\\x-3 < 2\\\\x < 5[/tex]
Solving the second inequality,
[tex]x+2 \leq 3x+5\\\\2 \leq 2x+5\\\\-3 \leq 2x\\\\-\frac{3}{2} \leq x[/tex]
So, the solution is [tex]-\frac{3}{2} \leq x < 5[/tex]
Jack has a rectangular piece of land, the area of which is represented by a₁ = 9.5%. His brother has a different rectangular piece of land, the area of which is represented by a2 = 14-). Let a represent the area in square meters and /represent the length in meters of the pieces of land. The two equations plotted on a graph meet at a point as shown in the image.
Answer:
yea that’s right
Step-by-step explanation:
Write the number below as a fraction in its simplest form
0.125 the 1 and 5 are recurring
If we write 0.125 in the fraction form then we will get 7/20.
Given Number which is 0.125
We are given a number 0.125 and we have to write this in fraction form.
0.125 can be written as 125/1000 it can be written as 7/20 by cutting on the numerator and denominator.
Fraction is a combination of numerator and denominator. If a fraction is solved then it comes in the decimal form. Recurring means the numbers which are coming again and again after the decimal.
In this fraction we have to ignore 1 and 5 because we have no idea how many times it is coming after decimal.
Hence the number 0.125 can be written as 7/20 in the fraction form.
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Donna took out a loan for $17,000 and was charged simple interest at an annual rate of 6.8% .
The total interest she paid on the loan was $867 . Do not round any intermediate computations.
Total amount she paid to repay her loan was $17,687
Amount is the total sum of money paid to the bank.It is basically the sum of interest and principal amount.
Principal is the sum of money taken from the bank
Interest is the sum of money charge by the bank during the period of loan repayment.
Rate of interest is the rate at which interest is charge in the principal sum
Time is the total period of the loan repayment.
Simple interest = (P x Rx T)/100
where, P=principal
R=rate of interest
T= time
Amount= Principal +Interest
As per question,
P=$17000
R=6.8%
I=$687
Amount=P+I
=$17000+687
=$17687
Therefore,Total amount she paid to repay her loan was $17,687
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answer a-d please!!!!!!!!!!!!!!!!
a) Intercepts are the points on the x and y axis
In the graph:
x-int: (-2,0), (2,0)
y-int: (0,1)
b) Domain is the list of x-values and Range is the list of y-values that make this graph true
Interval notations of domain and range
(Square brackets because the circles are closed)
Domain: [3,3]
Range: [0,3]
c) Intervals of increase and decrease: where the graph is increasing and decreasing
Increasing: -2 to 0 & 2 to 3
Decreasing: -3 to -2 & 0 to 2
d)Even, odd or neither
It is an even degree as both of its hands are facing upwards
Hope it helps!
Please help!
Julie wants to show that a quadrilateral with vertices J(2, 3), K(2,7), L(-2,7), M(-2,3) is a square. Using the distance formula, what should she find the length of each side to be?
8
4
3
2
Answer:
4 is the answer
Answer:
4 is the answer I believe
one phone company charged 65% of its normal long-distance rate after 5 p.m. A day-rate long-distance call from Houston to Chicago costs 20 cents per minute. How much is an 11-minute call between these two cities after 5 p.m. ?
The cost of 11-minute call between these two cities after 5 p.m is: 142.
CostGiven:
Charges for long distance=65% or .65
Cost=20 cents per minutes
Number of call minutes=11 minutes
Hence:
Cost =20 cents ×11 minutes times 0.65
Cost =143 cents
Therefore the cost of 11-minute call between these two cities after 5 p.m is: 142.
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Divide.
74.48 ÷ 7.6
Enter your answer as a decimal in the box.
What is breaking probation?
Answer:
a probation violation occurs when someone who has already been sentenced for a crime breaks the terms or conditions of that probation
Help I have no idea to do this!! I’m stuck!
Answer: 7
Step-by-step explanation:
[tex]A \cap C[/tex] denotes the intersection of A and C, or in other words, how many elements are shared between them.
The number of elements is 2 + 5 = 7
Which equation represents this number sentence?
Two more than one-third of a number is 8
Answer:
Step-by-step explanation:
One - third = 1/3
then:
one third of a number = a*1/3 = a/3
Then the equation that represents this sentence is:
2 + a/3 = 8
process:
a/3 = 8 - 2
a/3 = 6
a = 6*3
a = 18
Check:
2 + 18/3 = 8
2 + 6 = 8
n
Sigma 2k+4
k=1
4th term in sequence?
Answer:
12
Step-by-step explanation:
2k+4= 2*4 +4=8+4=12
hope it will help
Answer:
12
Step-by-step explanation:
Given:
[tex]\displaystyle \sum^n_{k=1}2k+4[/tex]
The 4th term in the sequence is when k = 4.
Therefore, substitute k = 4 into 2k + 4:
⇒ 2k+ 4 = 2(4) + 4
= 8 + 4
= 12
Therefore, the 4th term in the sequence is 12
A rectangular prism and a cylinder both have a height of 8m, and their cross-sectional areas are equal at every level parallel to their respective bases.
Complete the steps to find the prism.
1) [tex]V=lwh=5(x)(8)=\boxed{40x}[/tex]
2) [tex]V=\pi r^{2}h=(\pi)(3^{2})(8)=\boxed{72}\pi[/tex]
3) [tex]40x=72\pi\\\\x=\frac{72\pi}{40} \approx \boxed{5.7}[/tex]
