Answer:
[tex]\sin 253.740^{\textdegree} = -\frac{24}{25} = -0.960[/tex]
[tex]\cos 253.740^{\textdegree} = -\frac{7}{25} = -0.280[/tex]
[tex]\tan 253.340^{\textdegree} = \frac{24}{7} = 3.429[/tex]
Step-by-step explanation:
The point is in the 3rd Quadrant of the Cartesian Plane. Therefore, angle must be between 180° and 270° with respect to the horizontal.
The angle is:
[tex]\theta = 180^{\textdegree}+\tan^{-1}\left(\frac{24}{7} \right)[/tex]
[tex]\theta \approx 253.740^{\textdegree}[/tex]
The values of the trigonometrical functions are computed below:
[tex]\sin 253.740^{\textdegree} = -\frac{24}{25} = -0.960[/tex]
[tex]\cos 253.740^{\textdegree} = -\frac{7}{25} = -0.280[/tex]
[tex]\tan 253.340^{\textdegree} = \frac{24}{7} = 3.429[/tex]
At 5 feet tall, Emily casts a shadow that is 8 feet long. She is standing near a tree that casts a shadow that is 28 feet long. How tall is the tree?
Answer:
The tree is 17.5 ft tall
Step-by-step explanation:
We can use proportions to solve this.
Notice that Emily (5 feet tall) and her shadow (8 feet long) constitute the two legs of a right angle triangle (see attached image).
The nearby tree (unknown height H), will also cast a shadow (28 ft long) with the same inclination as Emily does due to the unique position of the sun relative to them.
Then we can use the proportion associated with the sides of similar triangles:
[tex]\frac{5\,ft}{8\,ft} =\frac{H}{28\,ft}[/tex]
Then, we can solve for H in the equation:
[tex]\frac{5\,ft}{8\,ft} =\frac{H}{28\,ft} \\H=\frac{28*5}{8} \,ft\\H=17.5 \.ft[/tex]
At a football game 100 students were surveyed about their food and drink purchases. Out of the 100 students surveyed, 70 bought a drink, 60 bought a food item, and 50 bought both a drink and a food item.
A student is chosen at random from the 70 students that bought a drink. What is the probability that the student also bought a food item?
Answer:
The probability is 5/7
Step-by-step explanation:
Please check the attached files for more explanation
The cylinder above has a radius of 5 inches and a height of 12 inches. What is the surface of the cylinder above?
Answer:
I think its b
Step-by-step explanation:
A=2πrh+2πr2=2·π·5·12+2·π·52≈534
Kyle drove his car 250 miles on 20 gallons of gas. How many miles per gallon did Kyle average?
Answer:
Step-by-step explanation:
250 divided by 20= 12.5
So 12.5 miles per gallon.
12.5. The answer ask for how many miles in 1 gallon. So, you do 250 divided by 20. 250 divided by 20 is 12.5, so he will drive 12.5 or 12 1/2 miles using each gallon of gas.
ANSWER : 12.5 or 12 1/2
Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x) and C(x) are in dollars.
R(x)= 2x, C(x)= 0.01x² + 0.4x + 30, when x=25 and dx/dt=7 units per day.
1. Find the rate of change of total revenue per day.
2. Find the rate of change of total cost per day.
3. Find the rate of change of total profit per day.
Answer:
1.- dR/dt = 14 $/day
2.- dC/dt = 4.55 $/day
3.- dP/dt = 7,7 $/day
Step-by-step explanation:
By definition Profit is equal to Revenue minus total costs then.
We have
R(x) = 2*x
C(x) = 0,01*x² + 0,4*x + 30
Then Profit P(x) = 2*x - 0,01*x² - 0,4*x - 30
P(x) = - 0.01*x² + 1.6*x - 30
1.- Find rate of change total revenue per day, when
x = 25 and dx/dt = 7 u/day
R(x) = 2*x
dR/dt = 2*dx/dt ⇒ dR/dt = 2* 7
dR/dt = 14 $/day
2.-
C(x) = 0,01*x² + 0,4*x + 30
dC/dt = 0,01*x* dx/dt + 0,4*dx/dt
dC/dt = 0,01*25*7 + 0.4*7
dC/dt = 1.75 + 2.8
dC/dt = 4.55 $/day
3.-
P(x) = - 0.01*x² + 1.6*x - 30
dP/dt = - 2*0,01*x*dx/dt + 1.6*dx/dt
dP/dt = - 2*0,01*25*7 + 1.6*7
dP/dt = - 3,5 + 11.2
dP/dt = 7,7 $/day
Answer:
The rate of change of total Revenue is $14 per day.The rate of change of total Cost is $4.55 per day.The rate of change of total Profit is $7.7 per day.Step-by-step explanation:
Given information
[tex]R(x)=2x\\C(x)=0.01x^2+0.4x+30[/tex]
When,
[tex]x=25\\dx/dt=7[/tex] units per day
As we know that
Profit = Revenue - Cost
Then, the Profit,
[tex]P(x)=2x-0.01x^2+0.4x-30\\P(x)=-0.01x^2+1.6x-30[/tex]
Now, The total Revenue per day
[tex]R(x)=2*x[/tex]
By differentiating both side with respect to [tex]t[/tex]
[tex]\\dR/dt=2*dx/dt\\dR/dt=2*7\\dR/dt=14[/tex]
Hence the rate of change of total revenue is $14 per day.
Similarly,
The total cost per day
[tex]C(x)=0.01x^2+0.4x+30[/tex]
By differentiating both side with respect to [tex]t[/tex]
[tex]dC/dT=0.01*x*dx/dt+0.4*dx/dt\\dC/dt=0.01*25*7+0.4*7\\dC/dt=1.75+2.8\\dC/dt=4.55[/tex]
Hence the rate of change of total cost is $4.55 per day
And the total Profit per day
[tex]P(x)=-0.01x^2+1.6x-30\\[/tex]
By differentiating both side with respect to [tex]t[/tex]
[tex]dP/dt=2*(-0.01)*x*dx/dt+1.6*dx/dt\\dP/dt=-2*(-001)*25*7+1.6*7\\dP/dt=-3.5+11.2\\dP/dt=7.7[/tex]
Hence the rate of change of total Profit is $7.7 per day
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The Martins plan for a garden is shown in the diagram. They need to figure out how much they will spend on topsoil for the garden. What is the area of the garden? The area of the garden is ft2. If topsoil costs $0.15 per square foot, how much will they spend to cover the area with topsoil? They will spend $.
answer 1 is : 144
Answer2:21.60
Answer:
144 and 21.60
Step-by-step explanation:
what is a diagonal matrix
Answer:
, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero
Step-by-step explanation:
Solve the equation 3x = 2x + 5.
What can you do to isolate the variable on one side of the equation?
What is the solution?
Answer:
x = 5
Step-by-step explanation:
To solve this equation for x, subtract 2x from both sides, obtaining:
x = 5.
The mean clotting time of blood is 7.45 seconds with a standard deviation of 3.6 seconds. What is the probability that an individual's clotting time will be less than 6 seconds or greater than 11 seconds? Assume a normal distribution. The probability is nothing.
The probability that an individual's clotting time will be less than 6 seconds or greater than 11 seconds, under a normal distribution with a mean of 7.45 and a standard deviation of 3.6, is approximately 50.9%.
Explanation:The subject in question pertains to the calculation of probabilities using the Normal Distribution. Given that the mean clotting time is 7.45 seconds with a standard deviation of 3.6 seconds, we need to find the probability that the clotting time will be either less than 6 seconds or more than 11 seconds.
First, we convert the clotting times to z-scores (the number of standard deviations away from the mean). The z-score for 6 seconds is (6-7.45)/3.6 = -0.40, and the z-score for 11 seconds is (11-7.45)/3.6 = 0.98. We can look these z-scores up in a Z-table to find the corresponding probabilities.
From the Z-table, we find that the probability of a z-score less than -0.40 is 0.345. The probability of a z-score less than 0.98 is about 0.836. Because we're asked to calculate the probability that the clotting time is either less than 6 seconds or greater than 11 seconds, we need to calculate the probabilities at the tails of the distribution. So we subtract the probability for 0.98 (0.836) from 1 to find the probability that clotting time is greater than 11 seconds, which is 0.164.
The probability of the clotting time being either less than 6 seconds or more than 11 seconds would be the sum of the two probabilities: 0.345 + 0.164 = 0.509 or 50.9%.
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The probability that an individual's blood clotting time is less than 6 seconds or greater than 11 seconds is approximately 0.5057, calculated using the Z-scores and the standard normal distribution.
The mean clotting time of blood is 7.45 seconds, with a standard deviation of 3.6 seconds. To find the probability that an individual's clotting time will be less than 6 seconds or greater than 11 seconds under normal distribution, we will use the Z-score formula:
Z = (X - mean) / standard deviation
For X = 6 seconds:For X = 11 seconds:Using Z-tables or standard normal distribution calculators:
P(Z < -0.40) ≈ 0.3446P(Z > 0.99) ≈ 0.1611Therefore, the total probability is:
P(X < 6 or X > 11) = P(Z < -0.40) + P(Z > 0.99) ≈ 0.3446 + 0.1611 = 0.5057
Consider the square spinner shown and assume all sections are the same size.
17
3
11
N
An experiment consists of spinning the spinner one time.
a. How many possible outcomes are there in the experiment?
b. What are the possible outcomes of the experiment?
c. List the sample space for the experiment.
d. Calculate P(z).
Answer:
a. 4 possible outcomes.
b. Possible outcomes - the spinner will fall on a 17, 3, 11 or N.
c. {17, 3, 11, N}
d. P(z) = 1/4.
Step-by-step explanation:
The probability of a specific value on one spin P(z) = 1/4.
a) There are four possible outcomes in the experiment.
b) The possible outcomes are 17, 3, 11, and N.
c) The sample space for the experiment is {17, 2, 11, N}.
d) P(z) = 1/4.
What is sample space?It is the total number of possible outcomes from a given set.
We have,
The square spinner has the following sections.
17, 3, 11, N.
Now,
a)
The number of possible outcomes.
= 17, 3, 11, N
= 4
b)
The possible outcomes are:
= 17, 3, 11, and N
c)
The sample space.
= {17, 3, 11, N}
d)
The probability of getting one specific outcome.
P(z) = 1/4
Thus,
The answers for a), b), c), and d) are given above.
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Sarina has two pieces of square paper. Each piece of paper has a side length of 7 inches. Both pieces of paper are cut along a diagonal, and the resulting triangles are arranged to form a new square, as shown below. What is the area of the new square?
Answer: 49
Step-by-step explanation:
If iTs half of each square its the same
Finding the Area of a Regular Polygon
The apothem of a regular hexagon measures
8 cm.
Which are true of the regular hexagon? Check all that
apply.
The perimeter of the hexagon is 48 cm.
The measure of the angle formed by the radius and
the apothem is 30°.
The side length of the hexagon is about 4.6 cm.
In a regular hexagon, the radius and side length are
equal in length.
The area of the hexagon is about 221.7 square cm.
8 cm
Intro
Done
Answer:
B, D and E.
just trust me
The angle made by the apothem and the radius would be; 30 degrees. Then the correct option is B.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
The apothem of a regular hexagon = 8 cm.
Then the side length of the hexagon will be
[tex]\rm x = \dfrac{8}{\sin 60^o}= 9.24\ cm[/tex]
The perimeter of the hexagon;
Perimeter = 6 × 9.24 = 55.43 cm
The area of the hexagon;
Area = 0.5 × 8 × 9.24 = 36.95 cm².
The angle made by the apothem and the radius = 30 degrees.
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Find the discriminant
9x^2+14x+13=8x^2
Answer:
The discrimant of this equation is 144.
Step-by-step explanation:
First you have to move all the variables to one side to make the equation/expression into 0 by substracting 8x² to both sides :
9x² + 14x + 13 = 8x²
9x² + 14x + 13 - 8x² = 8x² - 8x²
x² + 14x + 13 = 0
It is given that the formula of discriminant is, D = b² - 4ac where a&b&c represent the number of the equation, ax²+bx+c = 0 :
x² + 14x + 13 = 0
D = b² - 4ac
= 14² - 4(1)(13)
= 196 - 52
= 144
Final answer:
The discriminant of the quadratic equation 9x²+14x+13=8x² is found by simplifying to x²+14x+13=0 and using the formula b² - 4ac, yielding a result of 144.
Explanation:
The student's question involves finding the discriminant of the quadratic equation 9x² + 14x + 13 = 8x². We simplify this equation by subtracting 8x² from both sides, resulting in x² + 14x + 13 = 0.
The discriminant of a quadratic equation ax² + bx + c = 0 is given by b² - 4ac. For this equation, a = 1, b = 14, and c = 13. Substituting these into the discriminant formula gives (14)² - 4(1)(13) = 196 - 52 = 144.
Since the discriminant is positive, there are two distinct real roots to the equation. This could be relevant if we were to graph the equation, indicating where it crosses the x-axis, or if further solving for x was required.
Is 944544 divisible by 5?
Answer: No!
Step-by-step explanation:
Answer: No
Step-by-step explanation: If you take 944544 and divide it by 5, you will end up with 188908.8
2/3 - 1/2 =? please answer quick
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} - \frac{1}{2} =\frac{2x2}{3x3} -\frac{1x3}{2x3} =\frac{4}{6} -\frac{3}{6} =\frac{4-3}{6} =\frac{1}{6}[/tex]
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3}-\frac{1}{2}=\\ \\=\frac{2*2-1*3}{6}\\ \\=\frac{4-3}{6}\\ \\=\frac{1}{6}[/tex]
N office manager receives reports from employees via email. The probability model describes the number of emails the manager may receive in a day. Email Received 0 1 2 3 4 5 P(X) 0.05 0.15 0.35 0.25 0.15 0.05 How many emails would you expect the manager to receive each day?
Answer:
The correct answer is 2.45.
Step-by-step explanation:
Probability model of an office manager regarding reports from employees is given by:
X = 0; P(X) = 0.05
X = 1; P(X) = 0.15
X = 2; P(X) = 0.35
X = 3; P(X) = 0.25
X = 4; P(X) = 0.15
X = 5; P(X) = 0.05
Now expectation of number of emails that the manager would receive is given by X × P(X)
= 0 × 0.05 + 1 × 0.15 + 2 × 0.35 + 3 × 0.25 + 4 × 0.15 + 5 × 0.05
= 0 + 0.15 + 0.70 + 0.75 + 0.60 + 0.25
= 2.45
The correct answer is 2.45.
The calculation is as follows:
X = 0; P(X) = 0.05
X = 1; P(X) = 0.15
X = 2; P(X) = 0.35
X = 3; P(X) = 0.25
X = 4; P(X) = 0.15
X = 5; P(X) = 0.05
Now the number of emalis should be
= 0 × 0.05 + 1 × 0.15 + 2 × 0.35 + 3 × 0.25 + 4 × 0.15 + 5 × 0.05
= 0 + 0.15 + 0.70 + 0.75 + 0.60 + 0.25
= 2.45
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Need answer urgently please will give thanks and mark Brainliest
Answer:
D
Step-by-step explanation:
sqrt(7) = about 2.6
and that divided by 2 is
0.8 which means D is the Answer
A coffee business sells a pound of coffee for $ 9.75. Monthly expenses are $ 4,500 plus $ 4.25 for every pound of coffee sold. a. Write an IT function for total monthly income as a function of the number of pounds of coffee sold. b. Write a GT function for total monthly expenses as a function of the number of pounds of coffee sold. c. Write a function G for monthly profitability (profit) as a function of the number of pounds of coffee sold.
Answer:
a. IT = 9.75 * X
b. GT = 4500 + 4.25 * X
c. G = 9.75 * X - 4500 - 4.25 * X
Step-by-step explanation:
With the data of the statement we can get a function. Let X be the number of pounds sold.
to. Monthly income
IT = 9.75 * X
b. Monthly expenses
GT = 4500 + 4.25 * X
c. Monthly Earnings (Monthly Income - Monthly Expenses)
G = 9.75 * X - (4500 + 4.25 * X)
G = 9.75 * X - 4500 - 4.25 * X
a. The IT function should be = [tex]9.75 \times X[/tex]
b. The GT function is = [tex]4500 + 4.25 \times X[/tex]
c. The function G is = [tex]9.75 \times X - 4500 - 4.25 \times X[/tex]
Calculation of the functions:here we assume X be the number of pounds sold.
Since A coffee business should sell the coffee for $ 9.75. Monthly expenses are $ 4,500 along with $ 4.25 for each pound of coffee.
So,
a. The IT function is [tex]9.75 \times X[/tex]
b. The GT function should be [tex]4500 + 4.25 \times X[/tex]
c. The function G should be [tex]G = 9.75 \times X - (4500 + 4.25 \times X)[/tex]
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14 is what percent of 25?
Answer:
56%
Step-by-step explanation:
U reported me and the answer got deleted so
14:25*100 =
( 14*100):25 =
1400:25 = 56
here's your step by step explanation
and pls mark me brainliest
bye
Answer:
56%
Step-by-step explanation:
Is means equals and of means multiply. Let P be the percent
14 = P * 25
Divide each side by 25
14/25 = 25P/25
.56 = P
Change to percent form
56% =P
Solve: 3m - 2.4 = 6.6
Answer:
m=3
Step-by-step explanation:
i hope today brings you joy and happiness :)))
Answer:
The answer is 3
Step-by-step explanation:
This is how you solve it
3m-2.4=6.6
+2.4 . +2.4
3m=9
/3 . /3
m=3
Haley scored 3, 13, 15, 16, and 19 on five homework assignments. Her scores were based on a perfect score of 20. Which measure would be the most accurate to use to measure Haley's overall grade?
A) mean
B) median
C) mode
D) range
Answer:
median
Step-by-step explanation:
PLEASE HELP ME !!!
the expression 49x² - 36 is equivalent to :
(A) (7x - 6 )²
(B) (7x - 6 ) ( 7x + 6)
(C) (24.5x - 18 )²
(D) (24.5x - 18) (24.5x + 18 )
Answer:
(B) (7x - 6 ) ( 7x + 6)
Step-by-step explanation:
49x^2 - 36
This is the difference of squares
(7x)^2 - 6^2
We can factor this as
(a^2 -b^2) =(a-b) (a+b)
(7x)^2 - 6^2 = (7x-6) (7x+6)
How is multiplying exponents (x² ⋅ x⁴) different from raising a power to a power ((x²)⁴)?
Answer:
When you are "multiplying" exponents, you're really just adding them together. So in the case of (x² ⋅ x⁴), you add the exponents:
2 + 4 = 6
[tex]x^{6}[/tex] would be the answer.
On the other hand, raising a power to a power, is actually multiplying them. So it would just be:
2 ⋅ 4 = 8
[tex]x^{8}[/tex] would be the answer.
If you bought a cookie for 80¢ and paid for it with a 5 dollar bill, how much change would you receive?
Answer:
4 dollars and 20 cents
Step-by-step explanation:
5.00-.80=4.20
Answer:
$4.20
Step-by-step explanation:
What you bought will be subtracted from how much you paid with.
amount paid - amount bought
We paid for the cookie with $5, and bought something for 80 cents.
$5 is equal to 5.00, and 80 cents is equal to 0.8
5.00-0.8=4.2
So, you would get $4.20 back in change
Pablo is training for a marathon. He ran 5 4/8 miles on Friday, 6 5/8 miles on Saturday, and 7 4/8 miles on Sunday. How many miles did he run on all three days?
Answer:
19 5/8 miles
Step-by-step explanation:
First you convert all fractions into improper fraction which are
5 4/8 = 44/8
7 4/8 = 60/8
6 5/8 = 53/8
Then add just the numerators together as the denominator stays the same which looks like 157/8
Then see how many times 157 goes into 8 which is 19 with 5 left over
So you rewrite the answer as 19 5/8 miles
If I have 10
cups of cake batter to split amongst 18 cupcakes. How many cups of bafter will use for each cupcake?
⁵/₉ of bafter a cup would go per cupcake .
To determine how many cups of cake batter to use for each of the 18 cupcakes when you have 10 cups of batter, you need to divide the total amount of batter by the number of cupcakes.
Divide the total cups of batter (10 cups) by the number of cupcakes (18):
= 10 ÷ 18
≈ 10 / 18
Divide both sides by 2 to simplify and get:
= 5 / 9
Solve the riddle. Two-thirds of a number increased by five is the same as negative two-sixths of a number increased by fourteen. Two-thirds x + 5 = negative StartFraction 2 Over 6 EndFraction x + 14 What is the number?
Answer:
9Step-by-step explanation:
I got 100% on this assignment.The number in the equation is 9.
What is an equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation in algebra.
Let the number be x
(2/3)x + 5 = (-2/6)x + 14 (Equation given)
x( 2/3 + 2/6 ) = 14 - 5
x( 2/3 + 1/3) = 9
x = 9
Hence, the number in the given equation is 9
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find the size of angle XYZ
give your answer 1 decimal place
Answer:
23.6°
Step-by-step explanation:
The relevant trig relationship is ...
Sin = Opposite/Hypotenuse
This tells you ...
sin(Z) = XY/YZ = 6/15 = 2/5
The inverse sine (arcsine) function is used to find the angle when its sine is known.
Z = arcsin(2/5)
Z = 23.6°
To find the size of angle XYZ, we need additional information.
Explanation:To find the size of angle XYZ, we need additional information. Typically, to determine the size of an angle, we need to know the measures of other angles or the lengths of the sides of the triangle. If we have such information, we can use the trigonometric ratios or the properties of triangles to find the size of angle XYZ. Could you please provide the missing information?
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A car dealer raised the price of car form $10.500 to 11.000. what was the percent of change.
Answer:
4.5% (1dp)
Step-by-step explanation:
10500/11000x100=95.4545454545%
100-95.4545454545= 4.5454545455%
=4.5% (1dp)
I hope this helps!
Answer:
4.762%
Step-by-step explanation:
Change:
11,000 - 10,500 = 500
% change:
500/10500 × 100
100/21
4.761904762%
The parabola y=x^2 is reflected across the x-axis and then scaled vertically by the factor of 1/8. What is the equation of the new parabola?
Answer:
y = (-1/8)x^2
Step-by-step explanation:
Start with y = x^2. When the original parabola has been reflected across the x-axis, the pertinent equation becomes y = -x^2.
Now if this is scaled vertically by a factor of 1/8, we get:
y = (-1/8)x^2