Tshego's budget is more than R7200, then it would be enough to finish the tiling project. If his Budget is less than R7200, then it would not be enough.
We are not provided with any information in the question, so we cannot answer it as is. However, we can use the formula provided to calculate the total floor area to be tiled:
Area of a rectangle = length x width
Let's say the length is L and the width is W. Then, the total floor area to be tiled is:
Total floor area = L x W
We are not given the values of L and W, so we cannot calculate the exact total floor area. However, we can assume that Tshego has already calculated the total floor area to be 32 m².
To determine how many boxes of tiles Tshego will need, we need to know the size of each box of tiles and the total area that one box can cover. Let's assume that each box of tiles covers an area of 1 m².
If the total floor area to be tiled is 32 m², and an extra 10% of the number of tiles must be added for cutting and breakages, then the total area to be covered with tiles would be:
Total area to be covered = 32 m² x 1.1 = 35.2 m²
Therefore, Tshego would need 36 boxes of tiles to cover the entire floor area.
To determine if Tshego's budget is enough to finish the tiling project, we need to know the cost of each box of tiles and the total cost of the project. Let's assume that each box of tiles costs R200.
The total cost of the project would be:
Total cost = Number of boxes x Cost per box
Total cost = 36 x R200 = R7200
If Tshego's budget is more than R7200, then it would be enough to finish the tiling project. If his budget is less than R7200, then it would not be enough.
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Which function is represented by this graph?
-10 -8 -6 -4 -2
-10
-2
-6
-8
-10
2
4
6
8
10
The standard absolute value graph has been shifted 7 units to the right and 3 units down to get this graph.
That means we have answer B: f(x) = | x - 7 | - 3
Remember that the left-right shifts are opposite from what they would appear to be in the equation.
| x - 7 | shifts it right 7 units.
| x + 7 | shifts it left 7 units.
7. A card is randomly selected from a standard deck of cards. Write the theoretical
probability of each event as a fraction, decimal, and percent. [K:18)
a. A spade
b. A face card (jack, queen or king)
c. Not a face card
d. A black jack
e. A red or black card
f. A red face card
Answer:
a. The theoretical probability of drawing a spade from a standard deck of cards is 13/52, which reduces to 1/4, or 0.25, or 25%.
b. The theoretical probability of drawing a face card (jack, queen, or king) from a standard deck of cards is 12/52, which reduces to 3/13, or approximately 0.231, or 23.1%.
c. The theoretical probability of drawing a non-face card from a standard deck of cards is 40/52, which reduces to 10/13, or approximately 0.769, or 76.9%.
d. The theoretical probability of drawing a black jack from a standard deck of cards is 2/52, which reduces to 1/26, or approximately 0.038, or 3.8%.
e. The theoretical probability of drawing a red or black card from a standard deck of cards is 52/52, which reduces to 1/1, or 100%.
f. The theoretical probability of drawing a red face card from a standard deck of cards is 6/52, which reduces to 3/26, or approximately 0.115, or 11.5%.
I will give the BRAINIEST!!
It is 12pm and Maria and Nemzet are about to try and complete a jigsaw puzzle together before they have to get ready for a party that starts at Spes. If attempting this puzzle alone, it would take Maria 7
hours to complete it and it would take Nemzet 5 hours
Use the information above to choose all sentences which are true. Select all that apply
It will take them approximately 2.9 hours to finish the puzzle together. Therefore, options B, C are the correct answers.
Given that, Maria and Nemzet are about to try and complete a jigsaw puzzle.
Together attempting this puzzle alone, it would take Maria 7 hours to complete it and it would take Nemzet 5 hours
Here, 1/7 + 1/5 = 1/t
(5+7)/35 = 1/t
12/35 = 1/t
t=35/12
t=2.91
t=2.9 hours
Therefore, options B, C are the correct answers.
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PLEASE PLEASE HELP WILL MARK BRAINLIST!!!!!!!!!!!!
Answer:
y ≤ - [tex]\frac{2}{7}[/tex] x
Step-by-step explanation:
the blue region indicates where the solutions lie
that is below the given line
the equation of the line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 7, 2) ← 2 points on the line
m = [tex]\frac{2-0}{-7-0}[/tex] = [tex]\frac{2}{-7}[/tex] = - [tex]\frac{2}{7}[/tex]
the line crosses the y- axis at (0, 0 ) ⇒ c = 0
y = - [tex]\frac{2}{7}[/tex] x ← equation of line
the line is solid thus the region below is denoted by y ≤ , that is
y ≤ - [tex]\frac{2}{7}[/tex] x
2. Find the least number by which each of the given numbers should be multiplied so as to get a perfect square. Also, find the square root of the resulting number. a) 845 b) 1008
The least number by which each of the given numbers should be multiplied so as to get a perfect square are 5 and 7.
Here, we have,
we have
a) 845 =5×13×13
The smallest whole number is 5, by which 845 should be multiplied so as to get a perfect square.
Now , we get,
845 ×5=5×13×13×5
4225=5×13×13×5
√4225=65
b) 1008=2×2××2×3×3×3
The smallest whole number is 7, by which 1008 should be multiplied so as to get a perfect square.
Now , we get,
1008×7=2×2×2×2×3×3×7×7
7056=2×2×3×7
=84
Answer : 5 and 7
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What is the volume of the prism? 3ft. 1 1/2 ft. 6ft. Use the formula V=Bh to calculate the volume of the prism.
Answer:
18 ft.
Step-by-step explanation:
Which is equivalent to 49 2*
92x
0 gx
0 /g*
0 §g*
The expression that is equivalent to [tex]49^{\frac{3}{2}}[/tex] is given as follows:
D. 343.
What is the power of a power rule?The power of a power rule is used when a single base is elevated to multiple exponents.
Then the simplified expression is obtained keeping the base, while the exponents are multiplied.
The expression for this problem is given as follows:
[tex]49^{\frac{3}{2}}[/tex]
49 is the square of 7, hence:
49 = 7².
Then the expression can be simplified as follows:
[tex]7^2^{\frac{3}{2}}[/tex]
The multiplication of the exponents is of:
2 x 3/2 = 3.
(when we apply the power of power rule, we keep the base and multiply the exponents)
Hence:
7³ = 343.
Missing InformationThe problem is given by the image presented at the end of the answer.
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12,15,20,25,30,20,30,15,12,12
Answer:
The mode of this set of numbers is 12. If that is what you are looking for.
S
9. Is the square root of -68 a rational number?
Answer:
no, Irrational
Step-by-step explanation:
because the solution is a non-terminating decimal. 8.246
HELP ASAPPPPPP
Given: line AB with endpoints A2,5and B−4,−2.
Identify the coordinates of the midpoint.
Answer:
(-1, 1.5).
Step-by-step explanation:
To find the midpoint of line segment AB with endpoints A(2, 5) and B(-4, -2), you can use the midpoint formula. The midpoint formula states that the midpoint (M) of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by:
M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Let's calculate the midpoint using this formula:
x-coordinate of midpoint:
x = (2 + (-4)) / 2 = -2 / 2 = -1
y-coordinate of midpoint:
y = (5 + (-2)) / 2 = 3 / 2 = 1.5
Therefore, the midpoint of line AB is M(-1, 1.5).
Strontium-90 has a half-life of 28.1 years. How many years will it take for a sample of Strontium-90 to decay to 25% of its initial quantity?
Answer:
B
Step-by-step explanation:
One half life there will be 50 %
another half life and there will be 25 %
so TWO half lives * 28.1 yrs/ half life = 56.2 yrs
Find the missing information:
In the figure below, mZPSR = 106°. Find m PTR.
The arc angle in the circle is as follows:
mPTR = 63 degrees.
How to find measure of an arc angle?The tangent intersection theorem states that If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one-half the measure of its intercepted arc.
Therefore,
m∠PSR = 1 /2 (mPTR - mPR)
mPTR = ?
mPR = 149 degrees
m∠PSR = 106
Therefore,
106 = 1 / 2 (x - 149)
106 = 0.5x - 74.5
106 - 74.5 = 0.5x
31.5 = 0.5x
divide both sides by 0.5
x = 31.5 / 0.5
x = 63 degrees
Therefore,
mPTR = 63 degrees
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Ike, an investor, is considering opening a margin account and investing $1,000 in Mike’s mutual fund. The terms of the account require that he pay back the amount he borrowed on the margin by the end of the year with 10 percent interest. Ike is trying to decide what level of margin he wants. For example, if he chooses an account at the level of 50 percent, the bank will let him borrow and invest an additional $500, or 50 percent of his original $1,000. Complete the table below by filling in Ike’s account value at the end of the year, given varying levels of the margin account and mutual fund performance. Assume that Mike’s mutual fund will return 40 percent per year in a stellar market and 5 percent per year in a fair market, and that in a terrible market, it will lose 30 percent.
Answer:
Step-by-step explana
To fill in the table, we can use the following formula:
Account value at end of year = (Initial investment + amount borrowed) x (1 + interest rate) x (1 + mutual fund return rate)
Let's first calculate the amount borrowed based on the margin level:
50% margin level: $1,000 x 50% = $500 borrowed
75% margin level: $1,000 x 75% = $750 borrowed
100% margin level: $1,000 x 100% = $1,000 borrowed
Now, let's use the formula to fill in the table:
Margin level Mutual fund return Account value in stellar market Account value in fair market Account value in terrible market
50% 40% $1,500 $1,050 $525
50% 5% $1,100 $1,027.50 $717.45
50% -30% $700 $665 $465
75% 40% $1,750 $1,225 $612.50
75% 5% $1,312.50 $1,221.88 $853.63
75% -30% $875 $831.25 $581.88
100% 40% $2,000 $1,400 $700
100% 5% $1,500 $1,400 $980
100% -30% $1,000 $950 $665
Note that the account value in each market scenario is lower than the initial investment plus the amount borrowed. This is because Ike has to pay back the borrowed amount with interest at the end of the year. The interest rate is 10%, so the account value has to be higher than the initial investment plus the amount borrowed by at least 10% in order to make a profit.tion:
anyone know how to do this?
The center and variation of the data set is determined by calculating the mean and standard deviation.
The time spent volunteering is centered around 7 hours
The values differ from the average by about 4 hours.
What is a data set?A data set is described as a collection of data which corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the data set in question for tabular data sets.
The mean is found as:
Mean = (6 + 5 + 7 + 8 + 9) / 5 = 7 hours
The Range = maximum value - minimum value
Range = 9 - 5 = 4 hours.
The Deviations are (-1, -2, 0, 1, 2)
Standard deviation = √ [((-1)² + (-2)² + 0² + 1² + 2²) / 5]
Standard deviation = √ [(1 + 4 + 0 + 1 + 4) / 5]
Standard deviation = √2
Standard deviation = 1.4 hours
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Find the numerical value of the log expression.
log a = -10
log b = -10
log
a467
log c = 15
Answer:
150
Step-by-step explanation:
You want the numerical value for log(a, b, c) = (-10, -10, 15) of ...
[tex]\log\dfrac{\sqrt[3]{c^8}}{a^4b^7}[/tex]
Rules of logarithmsThe applicable rule of logarithms are ...
log(ab) = log(a) +log(b)
log(a^b) = b·log(a)
log(a/b) = log(a) -log(b)
RadicalsThe applicable rule for radicals is ...
[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]
ExpandedUsing the above rules, we can rewrite the logarithm as ...
[tex]\log\dfrac{\sqrt[3]{c^8}}{a^4b^7}=\dfrac{8}{3}\log(c)-(4\log(a)+7\log(b))\\\\=\dfrac{8}{3}(15)-(4(-10)+7(-10))=40+(4+7)(10)=\boxed{150}[/tex]
The numerical value of the log expression is 150.
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10. In this figure, a line through points X and Y will
A line through points X and Y will be perpendicular bisector of AB.
By examining the figure, it is evident that the compass created arcs as follows:
An arc was drawn with A as the center and a radius greater than half the length of AB.
and, another arc was drawn with B as the center using the same radius.
The points where these arcs intersect are labeled as X and Y.
This construction clearly represents the creation of a perpendicular bisector for the line segment AB.
Therefore, if we draw a line segment passing through points XY, it will serve as the perpendicular bisector of AB.
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The values listed are waiting times (in minutes) of customers at two different banks...
(a) The 99% confidence interval for the population standard deviation at Bank A is 1.33 to 2.16.
(b) The 99% confidence interval for the population standard deviation at Bank B is 1.41 to 2.29.
How to calculate the confidence interval?To find the confidence interval for the population standard deviation, we can use the chi-square distribution. The formula for the chi-square distribution is:
(X²) / (n-1) = s²
where X² is the chi-square value, n is the sample size, and s is the sample standard deviation.
For Bank A:
n = 20
s = 1.252
Using the chi-square distribution table with a degree of freedom of n-1 = 19 and a 99% confidence level, we find the critical values to be 8.907 and 32.852. Substituting these values into the formula above, we get:
(19 x 1.252²) / 32.852 < o² < (19 x 1.252²) / 8.907
1.78 < o² < 4.67
1.33 < o < 2.16
Therefore, the 99% confidence interval for the population standard deviation at Bank A is 1.33 to 2.16.
For Bank B:
n = 20
s = 1.397
Using the chi-square distribution table with a degree of freedom of n-1 = 19 and a 99% confidence level, we find the critical values to be 8.907 and 32.852. Substituting these values into the formula above, we get:
(19 x 1.397²) / 32.852 < o² < (19 x 1.397²) / 8.907
2.00 < o² < 5.24
1.41 < o < 2.29
Therefore, the 99% confidence interval for the population standard deviation at Bank B is 1.41 to 2.29.
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if a car left Lagos for portharcourt with the average speed of 60 km per hour, how long will it take for the car to arrive portharcourt?
Answer:
8 hours and 20 minutes
Step-by-step explanation:
Let's assume the distance between Lagos and Port Harcourt is approximately 500 kilometers. With an average speed of 60 km per hour, we can use the formula:
Time = Distance / Speed
Substituting the values, we get:
Time = 500 km / 60 km/h ≈ 8.33 hours
Therefore, it would take approximately 8 hours and 20 minutes for the car to travel from Lagos to Port Harcourt, assuming the distance is around 500 kilometers and the average speed is 60 km per hour. Please note that this is just an example calculation, and the actual time may vary depending on the distance and road conditions.
Name the acute angle in the shape
Answer:
∠ADB
Step-by-step explanation:
Acute angles measure less than 90°.
So, here ∠ADB is acute angle,
In recent years, Sheffield Transportation purchased three used buses.
This acquisition of used buses reflects Sheffield Transportation's commitment to providing reliable and cost-effective transportation options for their customers.
In recent years, Sheffield Transportation has acquired three used buses for their transportation fleet. The decision to purchase these buses was likely made to meet the growing demand for transportation services in the area, while also keeping costs down by opting for used vehicles instead of new ones.
It is important to note that when purchasing used buses, Sheffield Transportation would have had to ensure that the vehicles were in good condition and met safety standards before putting them into service. Overall, this acquisition of used buses reflects Sheffield Transportation's commitment to providing reliable and cost-effective transportation options for their customers.
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Help please answer the number 3 only thanyou
i will give brainliest
Answer:If cos(\theta) = \sqrt(3)/2, then we can use the Pythagorean identity sin^2(\theta) + cos^2(\theta) = 1 to find sin(\theta):
sin^2(\theta) + (\sqrt(3)/2)^2 = 1
sin^2(\theta) + 3/4 = 1
sin^2(\theta) = 1 - 3/4
sin^2(\theta) = 1/4
sin(\theta) = +/- 1/2
Since \theta is an acute angle, sin(\theta) must be positive. Therefore, sin(\theta) = 1/2.
We can then use the identity tan(\theta) = sin(\theta)/cos(\theta) to find tan(\theta):
tan(\theta) = sin(\theta)/cos(\theta)
tan(\theta) = (1/2)/(\sqrt(3)/2)
tan(\theta) = 1/\sqrt(3)
Finally, we can use the reciprocal and quotient identities to find the values of sec(\theta) and csc(\theta):
sec(\theta) = 1/cos(\theta)
sec(\theta) = 2/\sqrt(3)
csc(\theta) = 1/sin(\theta)
csc(\theta) = 2
Step-by-step explanation:
Answer:
[tex]\sin\theta=\dfrac{1}{2}[/tex]
[tex]\tan\theta=\dfrac{\sqrt{3}}{3}[/tex]
[tex]\csc\theta=2[/tex]
[tex]\sec\theta=\dfrac{2\sqrt{3}}{3}[/tex]
[tex]\cot\theta=\sqrt{3}[/tex]
Step-by-step explanation:
The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle:
[tex]\cos\theta= \sf \dfrac{adjacent}{hypotenuse}=\dfrac{\sqrt{3}}{2}[/tex]
Therefore, the length of the side adjacent angle θ is √3 and the length of the hypotenuse is 2.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
We can use Pythagoras Theorem to calculate the length of the side opposite angle θ:
[tex](\sqrt{3})^2+O^2=2^2[/tex]
[tex]3+O^2=4[/tex]
[tex]O^2=1[/tex]
[tex]O=1[/tex]
Therefore, the length of the side opposite angle θ is 1.
Now we have the lengths of the three sides of the right triangle, we can find the other trigonometric function of angle θ.
[tex]\boxed{\begin{minipage}{8cm}\underline{Trigonometric functions}\\\\$\sf \sin\theta=\dfrac{O}{H}\quad\cos\theta=\dfrac{A}{H}\quad\tan\theta=\dfrac{O}{A}$\\\\\\$\sf\csc\theta=\dfrac{H}{O}\quad\sec\theta=\dfrac{H}{A}\quad\cot\theta=\dfrac{A}{O}$\\\\\\where:\\\phantom{ww}$\bullet$ $\theta$ is the angle.\\\phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle.\\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse.\\\end{minipage}}[/tex]
Given values:
O = 1A = √3H = 2Substitute these values into the six trigonometric functions:
[tex]\sin\theta=\dfrac{O}{H}=\dfrac{1}{2}[/tex]
[tex]\cos\theta=\dfrac{A}{H}=\dfrac{\sqrt{3}}{2}[/tex]
[tex]\tan\theta=\dfrac{O}{A}=\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{3}}{3}[/tex]
[tex]\csc\theta=\dfrac{H}{O}=\dfrac{2}{1}=2[/tex]
[tex]\sec\theta=\dfrac{H}{A}=\dfrac{2}{\sqrt{3}}=\dfrac{2\sqrt{3}}{3}[/tex]
[tex]\cot\theta=\dfrac{A}{O}=\dfrac{\sqrt{3}}{1}=\sqrt{3}[/tex]
Lark's Donut Shop prepares 80 pounds of dough each morning. The bakers divide the dough evenly between glazed donuts and donut holes. They use 10 ounces of dough for each glazed donut and 2 ounces of dough for each donut hole. How many more donut holes than glazed donuts do the bakers make?
The Bakers make 85 glazed donuts.
To solve this problem, we need to determine how many glazed donuts and how many donut holes can be made from 80 pounds of dough. Then, we can compare the quantities of each to determine the difference.
First, we need to convert 80 pounds to ounces, since the amounts of dough for each type of donut are given in ounces. There are 16 ounces in a pound, so 80 pounds is equal to 80 x 16 = 1,280 ounces.
Next, we can set up two equations based on the amounts of dough needed for each type of donut:
Glazed donuts: 10 ounces of dough per donut
Donut holes: 2 ounces of dough per hole
Let's use "g" to represent the number of glazed donuts and "h" to represent the number of donut holes. We know that the total amount of dough used must be 1,280 ounces, so we can write:
10g + 2h = 1,280
We also know that the bakers divide the dough evenly between glazed donuts and donut holes, so the total number of donuts must be:
g + h = ?
We don't know the total number of donuts yet, but we do know that it must be an even number, since the dough is divided evenly between glazed donuts and donut holes.
To solve for g and h, we can use substitution or elimination. Let's use substitution. We can solve the first equation for one of the variables, such as h:
h = (1,280 - 10g) / 2
Then, we can substitute this expression for h in the second equation:
g + (1,280 - 10g) / 2 = ?
Simplifying this equation, we get:
g + 640 - 5g = ?
Combining like terms, we get:
5g + 640 = ?
Subtracting 640 from both sides, we get:
5g = -640
Dividing both sides by 5, we get:
g = -128
This doesn't make sense as a solution, since we can't have negative numbers of donuts. This means there must be an error in our calculations or assumptions.
Let's go back to the second equation:
g + h = ?
We know that the total number of donuts must be an even number, so we can write:g + h = 2n
where n is some positive integer. We can substitute this expression for g + h in the first equation:10g + 2h = 1,280
10g + 2(2n - g) = 1,280
Simplifying this equation, we get 14g - 4n = 1,28
Dividing both sides by 2, we get:7g - 2n = 640
Now we have two equations:7g - 2n = 640
g + h = 2n
We can use substitution or elimination to solve for g and h. Let's use elimination. We can multiply the first equation by 2 and add it to the second equation:14g - 4n = 1,280
2g + 2h = 4n
Multiplying the first equation by 2, we get:28g - 8n = 2,560
Adding this to the second equation, we get:30g = 2,560
Dividing both sides by 30, we get:g = 85.33
This means that the bakers make 85 glazed donuts. To find the number of donut holes, we can substitute this value
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The ratio of sailboats to dinghies in the bay was 5 to 7 if there were 70 sailboats in the bay how many dinghies were there?
Answer: 98
Step-by-step explanation:
sailboats to dinghies = 5 : 7
if 5 is 70 then what is 7 to ?
well 70/5 is 14 so we had to multiply 5 by 14 to get 70.
That means we also have to multiply 7 by 14 to get 98
2x+11y-5=0
What's slope and y intercept
Answer:
y = 5/11 is y-intercept. slope = -2/11
Step-by-step explanation:
2x + 11y - 5= 0
add 5 to both sides and subtract 2x from both sides
11y = 5 - 2x
to find y-intercept: make x = 0 (because all along the y-axis, x will be 0).
11y = 5 - 2(0)
= 5
divide by 11
y = 5/11. this is y-intercept.
to find slope (gradient):
11y = 5 - 2x
divide by 11
y = 5/11 - (2/11) x
slope = -2/11
Which point is represented by 6 times the quantity cosine 11 pi over 6 plus i times sine 11 pi over 6 end quantity question mark
[tex]6\left[\cos\left( \frac{11\pi }{6} \right) +i\sin\left( \frac{11\pi }{6} \right) \right] \\\\\\ 6\left[\cfrac{\sqrt{3}}{2}~~,~-\cfrac{1}{2}i \right]\implies (3\sqrt{3}~~,~-3i) ~~ \approx ~~ \stackrel{ \textit{\LARGE S} }{(5.2~~,~-3i)}[/tex]
Solve for the missing side length. Round to 2 decimal places
23°
6
X
The value of missing side is,
⇒ x = 2.54
We have to given that;
A triangle is shown.
And, To find the missing side of triangle.
Now, By using trigonometry formula, we get;
⇒ tan 23° = Opposite / Base
⇒ tan 23° = x / 6
⇒ 0.424 = x / 6
⇒ x = 0.424 × 6
⇒ x = 2.54
Thus, The value of missing side is,
⇒ x = 2.54
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Another right triangular prism has the same base as the prism in the example. The height of his prism is 8 m. What is the volume of the prism? Show your work
The first triangular prism has a height of 4
The length was x which was found out to be 10
And the width was 12
Here is the work shows for the first triangular prism
V=bh
240=(1/2)(x)(4)(12)
240=24x
10=x
Please help I give 25 brainly
The volume of the second right triangular prism is 7488.96 cubic meters.
For the second right triangular prism, we have:
Base: A right triangle with base 10 m and height 12 m
Height: 8 m
To find the volume, we can use the same formula as before:
Volume = (1/2) x base x height x altitude
Using the Pythagorean theorem, we can find that the altitude is:
altitude = √(10² + 12²) = √(244) ≈ 15.62
Now we can substitute the given values into the volume formula:
Volume = (1/2) x 10 x 12 x 8 x 15.62
Volume ≈ 7488.96 m^3
Therefore, the volume of the second right triangular prism is 7488.96 cubic meters.
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Help please I need to answer the questions a. b. c. d. e.
I would appreciate it.
The concentration will be 0.5 mg/L at time t =39.86 hours
To determine when the concentration will be 0.5 mg/L, we need to solve the equation:
c(t) = 0.5
20t/(t²+4) = 0.5
Multiplying both sides by (t²+4), we get:
20t = 0.5(t²+4)
Simplifying, we get:
20t = 0.5t² + 2
0.5t² - 20t + 2 = 0
Solving this quadratic equation using the quadratic formula, we get:
[tex]2\left(10+3\sqrt{11}\right)[/tex]
2(10+3(3.31))
2(10+9.93)
39.86
So the concentration will be 0.5 mg/L at t =39.86 hours
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Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml).
95 86 82 105 99 110 84 87
The sample mean is x ≈ 93.5. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that = 12.5. The mean glucose level for horses should be = 85 mg/100 ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use = 0.05.
What is the level of significance?
Compute the z value of the sample test statistic.
Find (or estimate) the P-value.
Since the P-value is less than the level of significance (0.0128 < 0.05), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that Gentle Ben has an overall average glucose level higher than 85.
How to determine the level of significanceThe level of significance is α = 0.05.
The test statistic is:
z = (x - μ) / (σ / √n)
where x is the sample mean,
μ is the population mean,
σ is the population standard deviation, and
n is the sample size.
Plugging in the given values, we get:
z = (93.5 - 85) / (12.5 / √8) ≈ 2.24
Using a standard normal distribution table or calculator, we find that the P-value is approximately 0.0128.
Since the P-value is less than the level of significance (0.0128 < 0.05), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that Gentle Ben has an overall average glucose level higher than 85.
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Need help please friends
The reduced row echelon form of the matrix is given as follows:
[tex]\left[\begin{array}{cccc}-1&0&0&8\\0&1&0&-2\\0&0&1&-6\end{array}\right][/tex]
How to obtain the reduced row echelon form?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{cccc}-1&5&-3&6\\0&3&6&-42\\0&-6&-1&18\end{array}\right][/tex]
First we want a value of 1 at line 1, column 1, hence we multiply the first line by -1, that is:
R1 -> -R1.
Hence:
[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&3&6&-42\\0&-6&-1&18\end{array}\right][/tex]
Then we want a value of 1 at line 2 column 2, thus:
R2 -> R2/3.
Hence:
[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&1&2&-14\\0&-6&-1&18\end{array}\right][/tex]
Then we want a value of 0 at line 3, column 2, hence:
L3 -> L3 + 6L2
[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&1&2&-14\\0&0&11&-66\end{array}\right][/tex]
Then the solution to the system of equations is given as follows:
11z = -66 -> z = -6.y + 2z = -14 -> y - 12 = -14 -> y = -2.x - 5y + 4z = -6 -> x + 10 - 24 = -6 -> x = 8.Hence the row echelon form of the matrix is given as follows:
[tex]\left[\begin{array}{cccc}-1&0&0&8\\0&1&0&-2\\0&0&1&-6\end{array}\right][/tex]
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