Answer:
X = 2² * 3² * 5³ * 7.
Step-by-step explanation:
140 = 2*2*5*7
15^2 = 3*5*3*5
So X = 2² * 3² * 5³ * 7
To find the prime factorization of X, we first need to simplify the expression.
140 × 15² = 140 × 225Now, we can factor 140 and 225 into their prime factors:
140 = 2² × 5 × 7225 = 3² × 5²So,
X = 140 × 225= (2² × 5 × 7) × (3² × 5²)We can now use the distributive property to multiply these factors together:
X = 2² × 3² × 5³ × 7Therefore, the prime factorization of X is:
Therefore, the prime factorization of X is:X = 2² × 3² × 5³ × 7Jacob is building a square pyramid for a class project. He needs to cover the entire pyramid in aluminum foil. The base of the pyramid has a perimeter of 76 centimeters. The slant height of each triangular side is 28 centimeters. What is the surface area, in square centimeters, of Jacob’s pyramid?
The surface area of the pyramid is 390.8 cm².
What is the surface area of the triangular pyramid?The surface area of the triangular pyramid is calculated as follows;
S.A = base area + ¹/₂ (perimeter + slant height)
The height of the pyramid is calculated by applying Pythagoras theorem;
h = √ (28² - 14²)
h = 24.2 cm
Area of the base = ¹/₂ x 28 cm x 24.2 cm = 338.8 cm²
The surface area of the pyramid is calculated as follows;
S.A = 338.8 cm² + ¹/₂ (76 cm + 28 cm)
S.A = 390.8 cm²
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Answer:
1,425
Step-by-step explanation:
I got this one correct
Evaluate the definite integral:
∫(e^z) + 8/ (e^z+8z)^2
The definite integral
[tex]-e^(2z)/u + 16e^z/u - 64ln(u)/u + C[/tex]
To evaluate this definite integral, we need to find the antiderivative of the integrand and evaluate it at the limits of
integration.
Let's start by using u-substitution:
Let [tex]u = e^z+8z[/tex]
Then [tex]du/dz = e^z+8[/tex]
And [tex]dz = 1/e^z+8 du[/tex]
Substituting this into the integral, we get:
[tex]∫(e^z) + 8/ (e^z+8z)^2 dz[/tex]
= [tex]∫(1/u^2)(e^z+8)^2 du[/tex]
= [tex]∫(1/u^2)(e^(2z)+16e^z+64) du[/tex]
= [tex]-e^(2z)/u + 16e^z/u - 64ln(u)/u + C[/tex]
Now we need to evaluate this antiderivative at the limits of integration.
Let's assume the limits are a and b:
= [tex][-e^(2b)/(e^b+8b) + 16e^b/(e^b+8b) - 64ln(e^b+8b)/(e^b+8b)] - [-e^(2a)/(e^a+8a) + 16e^a/(e^a+8a) - 64ln(e^a+8a)/(e^a+8a)][/tex]
Simplifying this expression is not easy, but it can be done with some algebraic manipulation.
Therefore, The definite integral
[tex]-e^(2z)/u + 16e^z/u - 64ln(u)/u + C[/tex]
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Drake was trying to write an equation to help him predict the cost of his monthly phone bill.
He is charged $35 just for having a phone, and his only additional expense comes from the number of text that he sends,
He is charged $0. 05 for each text. Name the function C(t), where C(t) is the cost of bill according to number of text.
The function for Drake's monthly phone bill, C(t), is C(t) = 35 + 0.05t, where t represents the number of texts sent.
Drake has two components to his monthly phone bill: the base cost of $35 and the additional cost for texts sent. The base cost is fixed, meaning it does not change, so we can represent it as a constant value in the function (35).
The cost per text is $0.05, which means it varies depending on the number of texts sent (t). To find the total cost (C(t)), we need to add the fixed cost ($35) and the variable cost ($0.05 times the number of texts). Therefore, the function representing Drake's monthly phone bill cost is C(t) = 35 + 0.05t.
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Lab tests of a new drug indicate a 70% success rate in completely curing the targeted disease. The doctors at the lab created the random data in the table using a representative simulation. The letter E stands for "effective," and N stands for "not effective. " (TL;DR: Each E stands for 'effective' and each N stands for 'not effective'. You need to calculate the ratio of Es to Ns in percentage. )
EEEE NEEE EEEE EEEN NEEN NEEE EENE NNNE NEEN EENE NENE EEEE EEEE NNNE ENEE NEEN ENEE EENN ENNE NEEE ENEN EEEE EEEN NEEE EENN EENE EEEN EEEE EENE EEEE ENEE ENNN EENE EEEE EEEN NEEE ENEE NEEE EEEE EEEE NENN EENN NNNN EEEE EEEE ENNN NENN NEEN ENEE EENE
The estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is [blank]. The estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is [blank]
a. The ratio of Es to Ns in percentage is 64%
b. Probability that it will take at least five patients to find one patient on whom the medicine would not be effective is impossible to estimate this probability from the table.
c. The probability that the medicine will be effective on exactly three out of four randomly selected patients is 12.9%
a. The total number of patients in the table is 50.
To calculate the ratio of Es to Ns in percentage, we count the number of Es and Ns and divide the number of Es by the number of Ns and Es combined, and then multiply by 100. Counting the table, we find that there are 32 Es and 18 Ns. So, the ratio of Es to Ns in percentage is:
32 / (32 + 18) * 100 = 64%
b. To estimate the probability that it will take at least five patients to find one patient on whom the medicine would not be effective, we need to look at the runs of Ns in the table. We can see that there are no runs of five or more Ns, so it is impossible to estimate this probability from the table.
c. To estimate the probability that the medicine will be effective on exactly three out of four randomly selected patients, we need to count the number of ways we can choose three Es and one N, and divide by the total number of possible outcomes of selecting four patients from the table. The total number of possible outcomes is:
50 choose 4 = 50! / (4! * (50-4)!) = 230300
The number of ways we can choose three Es and one N is:
32 choose 3 * 18 choose 1 = (32! / (3! * (32-3)!)) * (18! / (1! * (18-1)!)) = 32 * 31 * 30 / (3 * 2) * 18 = 32 * 31 * 30 * 18 / 6 = 297120
So, the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is:
297120 / 230300 ≈ 0.129 or about 12.9% (rounded to the nearest tenth of a percent).
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The roof of a building is in the shape of a hyperbola, y^2-x^2=38, where x and y are in meters. Determine the height of the outside. The distance between the center of the hyperbola and the walls is 3m.
a) -29. 1
b) 47. 3
c) 35. 2
d) 6. 9
The height of the outside is given as 17.44 meters
How to solveThe equation of hyperbola is :
[tex]y^2 - x^2 = 38[/tex]
=>[tex]y^2/38 - x^2/38 = 1[/tex]
(of the form [tex]y^2/a^2 - x^2/b^2 = 1[/tex] and transverse axis is y-axis.)
Here, [tex]a^2 = b^2 = 38[/tex]
[tex]c^2 = a^2 + b^2 = 38+38 = 76[/tex]
( a is the distance of vertices from the center and c is the distance of foci from the center.)
Distance between walls = 2 a = [tex]2*\sqrt(38) = 12.33[/tex] meters at the center
and = [tex]2c = 2*\sqrt(76) = 17.44[/tex] meters at the end when the line joining
end points of the wall on one side is through the foci point.
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Eric sells hot apple cider at the Hendersonville Apple Festival each year. For a batch of cider that makes 25 servings, Eric uses 2 tablespoons of cinnamon. How much cinnamon is in each serving of cider?
Each serving of cider contains 0.08 tablespoons of cinnamon.
Eric uses 2 tablespoons of cinnamon for a batch of cider that makes 25 servings. To find out how much cinnamon is in each serving, we need to divide the total amount of cinnamon used by the number of servings.
tablespoons/tablespoons= tablespoons per serving
2 tablespoons / 25 tablespoons = 0.08 tablespoons per serving
Therefore, there is 0.08 tablespoons of cinnamon in each serving of cider.
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The domain of g(x) = log 56 - x) can be found by solving the inequality
A. 6-x<0 ,B. 6-x>0,C. 6-x>=0, D. 6-x<=0
The inequality to solve is 56 - x > 0. The solution is x < 56. Therefore, the domain of the function g(x) is x < 56. So, the answer is option B.
The function is defined as g(x) = log(56 - x).
The domain of a logarithmic function is all the values that make the argument of the logarithm positive. In other words, the argument of the logarithm (56 - x) must be greater than 0.
So, we solve the inequality 56 - x > 0 for x
56 - x > 0
Subtract 56 from both sides
-x > -56
Divide both sides by -1, and remember to reverse the inequality
x < 56
Therefore, the domain of the function g(x) is all real numbers x such that x < 56. So, the correct answer is B).
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--The given question is incomplete, the complete question is given
" The domain of g(x) = log 56 - x) can be found by solving the inequality
A. 56-x<0 ,B. 56-x>0,C. 56-x>=0, D. 56-x<=0 "--
145 student are in the auditorium. Of the students in the auditorium, about 86% of the students play a sport. About 45% of the students are in the school play. How many students play a sport? How many students are in the play? Round your answer to the nearest whole
About 125 students play a sport and about 65 students are in the play.
To find the number of students who play a sport and those who are in the play, we need to use the given percentages and round the answers to the nearest whole.
Find the number of students who play a sport:
Multiply the total number of students (145) by the percentage of students who play a sport (86%).
145 × 0.86 = 124.7
Round the answer to the nearest whole number:
Approximately 125 students play a sport.
Find the number of students who are in the play:
Multiply the total number of students (145) by the percentage of students who are in the play (45%).
145 × 0.45 = 65.25
Round the answer to the nearest whole number:
Approximately 65 students are in the play.
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Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
40.7, my answer needs to be 20+ characters sooo....
I Need help with a Math Problem
please help find uv 10 points like ill actually do anything for someone to respond fast please!! im bad at math
Answer:
0.8660
Step-by-step explanation:
sin24=opposite ÷hypotenus
sin24=opposite ÷5
cross multiply
sin24x5=opposite
sin24=0.4067x5
opposite =0.8660
Select the correct answer from each drop-down menu. car model brake failure in new car a 0.0065% b 0.0037% c 0.0108% d 0.0029% e 0.0145% total 0.0048% the table gives the probabilities that new cars of different models will have brake failure. the car model that is least likely to have a brake failure is model , and the probability of brake failure for this model is %.
The car model that is least likely to have a brake failure is model d, and the probability of brake failure for this model is 0.0029%.
The given table provides the probabilities of brake failure for different car models. We need to identify the car model that has the lowest probability of brake failure and the corresponding probability.
From the table, we can see that the probability of brake failure is the lowest for model d, which is 0.0029%. To find this, we simply need to compare the probabilities given in the table and identify the smallest one.
It's worth noting that the total probability of brake failure across all car models is 0.0048%, which means that the probability of brake failure for any individual car model is quite low.
To express this in a more tangible way, we could say that out of 1000 new cars of model d, we can expect only about 2 or 3 to have brake failure. The low probabilities of brake failure suggest that new cars in general are quite safe and reliable when it comes to braking performance.
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Assume there are 0. 9 U. S. Dollars in a Canadian dollar. If gasoline costs 1. 50 Canadian dollars per liter, how many U. S. Dollars does it cost to buy a gallon of gas in Canada? (1 gallon = 3. 8 liters)
a. $3. 28
b. $5. 13
c. $2. 95
d. $5. 68
5.13 U. S. Dollars will it cost to buy a gallon of gas in Canada. The correct answer to the question is A
Given in the question,
Cost of 1 liter gasoline = 1.50 Canadian dollars
1 gallon = 3.8 liters
Thus, to calculate the price of 1 gallon we multiply the cost of 1 liter by 3.8
Cost of 3.8 liters of gasoline = 1.5 * 3.8
= 5.70 Canadian dollars
1 Canadian dollar = 0.9 U. S. dollars
5.70 Canadian dollars = 5.70 * 0.9
= 5.13 U. S. dollars
That is the cost of 1 gallon of gas in Canada is 5 U S dollars and 13 cents.
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PLS HELP ME WITH THIS!!!!
Answer:
g(x) = h(x -7) +5
Step-by-step explanation:
Given h(x) defines a parabola that opens upward with a vertex at (-2, -7) and g(x) defines the same parabola with its vertex at (5, -2), you want to express g(x) in terms of h(x).
TranslationThe graph of f(x) is translated right h units and up k units by ...
f(x -h) +k
We see that g(x) is a translation of h(x) right by 7 units and up by 5 units. This means (h, k) is (7, 5), and the translated function is ...
g(x) = h(x -7) +5
__
Additional comment
This is confirmed by the plots in the second attachment.
Answer: g(x)=h(x-7) +5
Step-by-step explanation:
The graph g(x) has been shifted up 5 (+5) and right 7
When shift a function, the y change, up/down, goes at end of function
When shift in x direction happens, you take opposite sign so we will do -7
g(x)=h(x-7) +5
Kristen is trying to determine the x-intercepts of the graph of a quadratic function. Which form would be the most beneficial in order for Kristen to quickly identify the coordinates? A. Standard Form B. Intercept Form C. Vertex Form
The form in which is easier to identify the x-intercepts is the one in option B. Intercept form.
Which form would be the most beneficial in order for Kristen to quickly identify the coordinates?If a quadratic equation has a leading coefficient a and x-intercepts x₁ and x₂, then the quadratic equation can be written as:
y = a*(x - x₁)*(x - x₂)
That is called the factored form or the intercept form.
Notice that if the quadratic equation is written in that form, is really easy to identify the x-intercepts of the equation, then that would be the most beneficial form in order for Kristen to quickly identify the coordinates, the correct option is B.
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Solve systems of equation by the substitution method.
a - 3 = 2b
4a + 5b- 8 = 0
The value of the variables are a = 1 and b = -1
How to solve the equationGiven that the equations are;
a - 3 = 2b
4a + 5b- 8 = 0
Using the substitution method, we have;
Make 'a' the subject of formula from equation (1)
a = 2b + 3
Now, substitute the value of the variable in the second equation
4(2b + 3) + 5b - 8 = 0
expand the bracket, we have;
8b + 12 + 5b - 8 = 0
collect the like terms, we get;
8b + 5b = 0 - 5
add or subtract the values
5b = -5
b = -1
Substitute the value of b as =-1
a = 2(-1) +3
expand the bracket
a = -2 + 3
a = 1
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Can someone help me asap? It’s due today!!
John would have the option of taking 10 different cones
How to solve for the coneThe questions says that there is the option of having the flavors that are available ice cream flavors are: chocolate (C), mint chocolate chip (M), strawberry (S), rainbow sherbet (R), and vanilla (V).
The available flavors are then 5 in number
Then the number of scoops that he can have from each of the cone is said to be 2
Hence we would have 5 x 2
= 10
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The final exam scores in a statistics class were normally distributed with a mean of
63 and a standard deviation of five.
find the score that marks the 11% of all scores.
The score that marks the 11% of all scores is approximately 56.875 .
To find the score that marks the 11% of all scores, we need to use the standard normal distribution table, also known as the Z-table, since the given distribution is a normal distribution.
The first step is to find the Z-score that corresponds to the 11th percentile, which is given by: Z = invNorm(0.11) ≈ -1.225
Here, "invNorm" represents the inverse of the standard normal cumulative distribution function, which can be computed using statistical software or a calculator.
The second step is to use the Z-score formula to find the raw score that corresponds to this Z-score:Z = (X - μ) / σ
where X is the raw score we want to find, μ is the mean of the distribution, and σ is the standard deviation. Plugging in the values we have:
-1.225 = (X - 63) / 5
Solving for X, we get:
X = -1.225 * 5 + 63 = 56.875
Therefore, the score that marks the 11% of all scores is approximately 56.875
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A boat travels a straight route from the marina to the beach. The marina is located at point (0,0) on a coordinate plane, where each unit represents 1 mile. The beach is 3. 5 miles east and 4 miles south from the marina. Use the positive y-axis as north. What is the distance the boat travels to get to the beach? Round your answer to the nearest tenth. *
The distance the boat travels to get to the beach is approximately 5.0 miles.
To see why, we can draw a right triangle on the coordinate plane, with one leg along the x-axis (going 3.5 miles east) and the other leg along the y-axis (going 4 miles south). The hypotenuse of this triangle is the straight distance from the marina to the beach, which is the distance the boat travels.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
c^2 = a^2 + b^2
c^2 = (3.5)^2 + (4)^2
c^2 = 12.25 + 16
c^2 = 28.25
c ≈ 5.0
Therefore, the distance the boat travels to get to the beach is approximately 5.0 miles.
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En un viaje en mula hacia el pico duarte el jinete observa en un poste 1, 290 m sobre el nivel del mar , luego de 5 horas de camino presta atencion a otro poste que indica , 2, 480 m sobre el nivel de mar. ¿ cual ha sido su desplazamiento en direccion vertical?
The vertical displacement of the mule comes out to be the difference between the final and the initial position which is 1190 m.
The displacement refers to the distance between the final and the initial position of an object. It is the shortest distance between these points is the displacement of the object. It is a vector quantity.
Vector quantity refers to the measurement in which both magnitude and direction are considered.
Starting point = 1290 m
Final point = 2480 m
Displacement = 2480 - 1920
= 1190 m
1190 m is the vertical displacement of the mule when traveling from one post to another.
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The question is in Spanish and when translated to English, it is:
On a mule trip to Duarte Peak, the rider observes a post 1,290 m above sea level, after 5 hours of walking he pays attention to another post that indicates 2,480 m above sea level. What has been its displacement in the vertical direction?
I have some coins in my pocket. Nickles and pennies I have a total of $. 41 I have 21 coins in total. How many Nickles and pennies do I have?
The number of nickels and pennies in the pocket is 5 and 16 respectively.
How to find the number of coins?To find the number of coins, Let's assume the number of nickels is x and the number of pennies is y.
According to the problem, we have two equations:
The total value of the coins is $0.41:
0.05x + 0.01y = 0.41
The total number of coins is 21:
x + y = 21
Now we can solve this system of equations to find x and y. One way to do this is to use substitution.
Solving the second equation for y, we get:
y = 21 - x
Substituting this into the first equation, we get:
0.05x + 0.01(21 - x) = 0.41
Simplifying:
0.05x + 0.21 - 0.01x = 0.41
0.04x = 0.2
x = 5
So we have 5 nickels.
Substituting this into the equation y = 21 - x, we get:
y = 21 - 5 = 16
So we have 16 pennies.
Therefore, the number of nickels and pennies in the pocket is 5 and 16 respectively.
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If a couch measures 10ft across in real life, what would it's measurement be in the scale drawing (in)
Explain
the measurement of the couch in the scale drawing would be 15 inches.
what is scale drawing?We can precisely portray locations, areas, structures, and details in scale drawings at a scale that is either smaller or more feasible than the original.
When a drawing is said to be "to scale," it signifies that each piece is proportionate to the real or hypothetical entity; it may be smaller or larger by a specific amount.
When something is described as being "drawn to scale," we assume that it has been printed or drawn to a conventional scale that is accepted as the norm in the construction sector.
When our awareness of scale improves, we are better able to quickly recognize the spaces, zones, and proposed or existent spatial relationships when looking at a drawing at a given scale.
One metre is equivalent to one metre in the actual world. When an object is depicted at a 1:10 scale, it is 10 times smaller than it would be in real life.
You might also remark that 10 units in real life are equivalent to 1 unit in the illustration.
To determine the measurement of the couch in the scale drawing, we can use the scale factor provided:
1/4 inch = 2 feet
This means that every 1/4 inch in the drawing represents 2 feet in real life.
To find the measurement of the couch in the drawing, we need to convert its actual size to the corresponding size in the drawing using the scale factor.
First, we can convert the actual size of the couch to feet:
10 ft = 10 ft x 12 inches/ft = 120 inches
Next, we can use the scale factor to convert the actual size to the corresponding size in the drawing:
1/4 inch = 2 feet
1 inch = 8 feet (multiplying both sides by 4)
So, 120 inches in real life is equal to:
120 inches / 8 feet per inch = 15 inches in the drawing
Therefore, the measurement of the couch in the scale drawing would be 15 inches.
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Last year, the revenue for medical equipment companies had a mean of 70 million dollars with a standard deviation of 13 million. Find the percentage of companies with revenue between 50 million and 90 million dollars. Assume that the distribution is normal. Round your answer to the nearest hundredth
The percentage of companies with revenue between 50 million and 90 million dollar is: 87.6%
How to find the percentage from z-scores?The formula for the z-score in this type of distribution is:
z = (x' - μ)/σ
where:
x' is sample mean
μ is population mean
σ is standard deviation
We are given:
μ = 70 million dollars
σ = 13 million dollars
Thus:
When x' = 50 million dollars, we have:
z = (50 - 70)/13
z = -1.54
When x' = 90 million dollars, we have:
z = (90 - 70)/13
z = 1.54
Using probability between two z-scores calculator, we have:
z = 0.87644 = 87.6%
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tony collected data on the years of employment and the annual salaries of the salespeople at company z. he made a scatterplot and drew a trend line that approximates the line of best fit for the data, as shown below.Tony expects his salary to be about $70,000 after he has been employed as a sales person at company z for 15 years. use the trend line and slope to explain whether tony's salary expectation is reasonable.
Based on the trend line and slope, Tony's expected salary of $70,000 after 15 years of employment at Company Z is reasonable, as it falls within the range of salaries predicted by the line of best fit.
First, we need to find the equation of the trend line. To do this, we use the least squares regression method to find the line that best fits the data. Let x be the years of employment and y be the annual salary. We can calculate the slope and y-intercept of the trend line using the following formulas
slope = (nΣ(xy) - ΣxΣy) / (nΣ(x²) - (Σx)²)
y-intercept = (Σy - slopeΣx) / n
where n is the number of data points, Σ represents the sum of, and ( )² denotes squared.
We can use the given data to calculate the values needed for the formulas. Let's denote the years of employment as x and the annual salary as y.
x: 1 2 3 4 5 6
y: 45 50 55 60 65 70
n = 6
Σx = 1 + 2 + 3 + 4 + 5 + 6 = 21
Σy = 45 + 50 + 55 + 60 + 65 + 70 = 345
Σxy = (145) + (250) + (355) + (460) + (565) + (670) = 1305
Σ(x²) = 1² + 2² + 3² + 4² + 5² + 6² = 91
Now we can plug these values into the formulas to find the slope and y-intercept
slope = (61305 - 21345) / (691 - 21²) = 5
y-intercept = (345 - 521) / 6 = 20
We can write the equation of the trend line in the form y = mx + b, where m is the slope and b is the y-intercept
y = 5x + 20
Finally, we can use this equation to estimate Tony's salary after 15 years of employment
y = 5(15) + 20 = 95
Based on the trend line and slope, we would expect Tony's salary to be about $95,000 after 15 years of employment.
This is higher than his expected salary of $70,000, so it may not be a reasonable expectation. However, it's important to note that the trend line is just an approximation and there may be other factors that could affect Tony's salary.
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Find the length of side a given a = 50°, b = 20, and c = 35. round to the nearest whole number.
The length of side a is 50 if the angle ∠bac is 50° and the length of side b is 20 and side c is 35 using cosine law.
Length of side b = 20
Length of side c = 35
Angle ∠bac = 50°
To calculate the length of the side a, we need to use the cosine law. The formula is:
[tex]a^2 = b^2 + c^2 - 2bc cos(A)[/tex]
Substituting the given values in the formula, we get:
[tex]a^2 = 20^2 + 35^2 - 2(20)(35)cos(50°)[/tex]
[tex]a^{2}[/tex] = 400 + 1225 + (1400)*(0.642)
[tex]a^{2}[/tex] = 1625 + 898.8
a = [tex]\sqrt{2523.8}[/tex]
a = 50
Therefore we can conclude that the length of side a is 50 using cosine law.
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A 5-minute international call costs $2.15 and a 12-minute call costs $3.06. The work shows how to write an equation where x represents the number of minutes, and y represents the total cost of an international call. Analyze the steps of the work to determine if the equation is correct.
1. Point 1: (5, 2.15). Point 2: (12, 3.06). 2. m = StartFraction 12 minus 5 Over 3.06 minus 2.15 EndFraction = StartFraction 7 Over 0.91 EndFraction = 7.69. 3. 5 = 2.15 (7.69) + b. b = negative 11.54. 4. y = 7.69 x minus 11.54.
In which step did Emilia make an error?
In step 2, she substituted the x values for y and the y values for x.
In step 3, she didn’t use an x and y from the same coordinate pair.
In step 4, Emilia solved for the wrong variable.
Emilia did not make an error.
Emilia make an error in step 3 she didn't use an x and y from the same coordinate pair.
In step 1 : point 1 : (5, 2.15) point 2 : (12, 3.06)
In step 2 : m = [tex]\frac{12-5}{3.06-2.15}[/tex]
m = 7/0.91
m = 7.69
In Step 3 : y = mx + b
m = slope
Point used by Emilia (2.15 , 5)
But the point should be used be Emilia is (5, 2.15)
2.15 = 5(7.69) + b
b = y intercept
b = -36.3
step 3 is wrong she didn't use right coordinates of x and y
In step 4 : y = mx +b
y = 7.69x -36.3
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The Volume, V, in liters, of air in the lungs is approximated by the the model, V = -0.0374+3 +0.1525+2 +0.1729t, during a five second respiratory cycle. In here, t is measured in second
The model approximates the volume, V, in liters, of air in the lungs during a five-second respiratory cycle using the equation V = -0.0374t + 3 + 0.1525t^2 + 0.1729t.
The given equation represents a mathematical model for estimating the volume of air in the lungs during a respiratory cycle. It is a quadratic equation with three terms: -0.0374t, 0.1525t^2, and 0.1729t.
The term -0.0374t represents the linear decrease in volume over time, indicating that the volume decreases by 0.0374 liters for every second of the respiratory cycle.
The term 0.1525t^2 represents the quadratic relationship between volume and time squared, indicating that the rate of change of volume with respect to time is influenced by the square of time.
The term 0.1729t represents the linear increase in volume over time, indicating that the volume increases by 0.1729 liters for every second of the respiratory cycle.
Overall, this model provides an approximation of the volume of air in the lungs during a five-second respiratory cycle, taking into account both linear and quadratic relationships with time.
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(Linear Systems: Applications). Find a polynomial p(2) of degree three such that
7(-2)=3,P(-1)=3,7(1)=-9,8(2)=-33.
Therefore, the polynomial p(x) that satisfies the given conditions is:
p(x) = ax^3 + bx^2 + cx + d
p(x) = x^3 - 2x^2 + 3x + 23
So, p(2) = 1(2)^3 - 2(2)^2 + 3(2) + 23 = 9.
To find a polynomial p(2) of degree three, we need four pieces of information. We can use the given values to set up a system of linear equations:
-7a + 2b - 4c + d = 3
-a - b + c - d = 3
7a + b + c + d = -9
8a + 4b + 2c + d = -33
We can solve this system using any method of linear algebra. One way is to use row reduction:
[ -7 2 -4 1 | 3 ]
[ -1 -1 1 -1 | 3 ]
[ 7 1 1 1 | -9 ]
[ 8 4 2 1 | -33 ]
R2 + R1 -> R1:
[ -8 1 -3 0 | 6 ]
[ -1 -1 1 -1 | 3 ]
[ 7 1 1 1 | -9 ]
[ 8 4 2 1 | -33 ]
R3 - 7R1 -> R1, R4 - 8R1 -> R1:
[ -8 1 -3 0 | 6 ]
[ 0 -7 8 -1 | 51 ]
[ 0 -4 4 1 |-51 ]
[ 0 4 26 1 |-81 ]
R4 + R2 -> R2:
[ -8 1 -3 0 | 6 ]
[ 0 -3 34 0 | 30 ]
[ 0 -4 4 1 |-51 ]
[ 0 4 26 1 |-81 ]
R3 + (4/3)R2 -> R2:
[ -8 1 -3 0 | 6 ]
[ 0 -3 34 0 | 30 ]
[ 0 0 50 4 |-11 ]
[ 0 4 26 1 |-81 ]
R4 - (4/3)R2 -> R2, R3 - (5/6)R2 -> R2:
[ -8 1 -3 0 | 6 ]
[ 0 -3 34 0 | 30 ]
[ 0 0 8 4 |-34 ]
[ 0 0 8 1 |-103 ]
R4 - R3 -> R3:
[ -8 1 -3 0 | 6 ]
[ 0 -3 34 0 | 30 ]
[ 0 0 8 4 |-34 ]
[ 0 0 0 -3 |-69 ]
Now we can back-substitute to find the coefficients of the polynomial:
d = -69/(-3) = 23
c = (-34 - 4d)/8 = 3
b = (30 - 34c + 3d)/(-3) = -2
a = (6 + 3b - 3c + d)/(-8) = 1
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List the defining attributes of each 3-D figure. Then name the figure.
Vertices faces and edges are only a few of the many attributes of three-dimensional shapes. The 3D shapes' faces are their flat exteriors. An edge is the section of a line where two faces converge.
List out the attributes of 3-D figures.1) cube
A vertex is the intersection of three edges. A solid or three-dimensional form with six square faces is called a cube. These are the characteristics of the cube.
Every edge is equal.
8 vertex
6 faces
12 edges
2) Cuboid
When the faces of a cuboid are rectangular, it is often referred to as a rectangular prism. The angles are all 90 degrees each. It has a cuboid.
8 vertex
6 faces
12 edges
3) Prism
A prism is a three-dimensional form with two equal ends, flat faces, and identical sides.l cross-section down the length of it. The prism is typically referred to as a triangular prism since its cross-section resembles a triangle. There is no bend to the prism. A prism has also
6 vertex
9 edges
2 triangles and 3 rectangles
5 faces.
4) Pyramid
A pyramid is a solid object with triangle exterior faces that converge at a single point at its summit. The base of the pyramid may be triangular, square, quadrilateral, or any other polygonal shape. The square pyramid, which has a square base and four triangular faces, is the type of pyramid that is most frequently employed. Take a look at a square pyramid.
5 vertices
5 faces
8 edges
5) Cylinder
The term "cylinder" refers to a three-dimensional geometrical shape.two circular bases joined by a curving surface make up this figure. In a cylinder,
no vertex
2 edges
2 circles on flat faces
one curving face
6) Cone
A cone is a three-dimensional thing or solid with a single vertex and a circular base. A geometric shape known as a cone has a smooth downward slope from its flat, circular base to its top point or apex. In a cone
one vertex
1 edge
1 circle with a flat face.
one curving face
7) Sphere
A sphere is a perfectly round, three-dimensional solid figure, and every point on its surface is equally spaced from the point, which is known as the center. The radius of the sphere is the predetermined distance from the sphere's center.
a sphere is
zero vertex
zero edges
one curving face
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The graph shows f(x). The absolute value function g(x) is described in the table. The graph shows a v-shaped graph, labeled f of x, with a vertex at 0 comma 2, a point at negative 1 comma 3, and a point at 1 comma 3. x g(x) −1 5 0 4 1 3 2 2 3 3 If g(x) = f(x + k), what is the value of k? k = −2 k is equal to negative one half k is equal to one half k = 2
Where the above graph and conditions are given, the value of k that satisfies g(x) = f(x+k) is k = -2.
What is the explanation for the above response?We can determine the value of k by using the given relationship between g(x) and f(x+k).
If g(x) = f(x + k), then we can substitute the given values of x in g(x) to get:
g(-1) = f(-1 + k) --> 5 = f(-1 + k)
g(0) = f(0 + k) --> 4 = f(k)
g(1) = f(1 + k) --> 3 = f(1 + k)
g(2) = f(2 + k) --> 2 = f(2 + k)
g(3) = f(3 + k) --> 3 = f(3 + k)
We know that f(x) is a v-shaped graph with a vertex at (0,2) and points at (-1,3) and (1,3). Therefore, we can conclude that f(k) = 4, which means that k is the x-coordinate of the vertex of f(x) shifted to the left or right.
Since the vertex of f(x) is at (0,2), and the x-coordinate of the vertex of f(x+k) is at k, we have:
k = 0 --> vertex of f(x+k) is at (0,2)
k = -1 --> vertex of f(x+k) is at (-1,2)
k = 1 --> vertex of f(x+k) is at (1,2)
k = 2 --> vertex of f(x+k) is at (2,2)
Therefore, the value of k that satisfies g(x) = f(x+k) is k = -2.
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