The value of given data, (2^5/3)^60% can be calculated by simplification as 4.138.
Define the term percentage?A fraction or decimal is multiplied by 100 to become a percentage. To convert 0.75 to a percentage, for instance, multiply it by 100, which results in 75%. Similar to how 3/5 can be converted to a percentage, 3/5 can be expressed as 60% by multiplying by 100 and then dividing by 5 to get 0.6.
In a variety of areas, including banking, statistics, science, and daily life, percentages are utilized. They are frequently used to convey proportions, relative values, and rates of change.
We have the value;
⇒ (2⁵/3)^60% or we can write that; \((\frac{32}{3}) ^{0.6}\)
⇒ \((10.66) ^{0.6}\)
⇒ 4.138
Therefore the value of given data is 4.138
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Para resolver esta expresión, primero debemos calcular la potencia dentro de los paréntesis.
2^5/3 = (2^5)^(1/3) = 2^(5/3)
Entonces, nuestra expresión se convierte en:
(2^(5/3))^60%
Para simplificar esto, convertimos el exponente del 60% en una fracción:
60% = 60/100 = 3/5
Ahora podemos usar la propiedad de potencias de exponentes para multiplicar los exponentes:
(2^(5/3))^60% = 2^((5/3)*(3/5)) = 2^1 = 2
Por lo tanto, la respuesta es 2.
Which of the following best describes continuous data? Numerical data which can have any value on a specific range Numerical data where the values are whole numbers Categorical data where the groups have no order
Continuous data is numerical data that can have any value within a specific range. It is not restricted to whole numbers and can take on any decimal or fractional value within the range of measurement.
Continuous data is characterized by its ability to be measured and divided into smaller units, allowing for a more precise representation of the data. It is typically represented on a continuous scale or axis, such as a number line. Examples of continuous data include measurements such as height, weight, temperature, time, and distance.
In contrast, categorical data consists of distinct groups or categories with no inherent order, while numerical data that consists only of whole numbers is known as discrete data. Continuous data, on the other hand, allows for infinite possibilities between any two points, making it a more flexible and detailed form of numerical data.
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What is the slope of the line with the following coordinates from the
table?
Answer: The slope is 1/8
Step-by-step explanation:
The x values go up by 8. That gives the run.
the y values go up by 1. That gives the rise.
Slope is rise/run SO
1/8 is the slope.
Graph attached.
Y= 1/2x-3
Slope (m)=
Y-intercept (b) =
Which do we use first?
slope (m) = 1/2
y-intercept (b) = -3
You use the y-intercept first to find the first point of (0, -3). From there you can use the slope to find the other points.
This is a math question if you are good this is good for you this is hard
Answer:
Hope this helps!
Step-by-step explanation:
1- -24
2- -23
3- -2
4- 11
5- 5
6- -3
7- 28
8- 120
The probability of any plant surviving in Kerry's garden is 0. 8. Suppose she plants 19 new plants this year. A) What is the probability that at least 14 of them survive
The probability of any plant surviving in Kerry's garden is 0. 8. If she plants 19 new plants this year then the probability of at least 14 out of 19 plants surviving is 0.1082.
The probability of any plant surviving in Kerry's garden is 0.8. Suppose she plants 19 new plants this year.
A) What is the probability that at least 14 of them survive?
To find the probability of at least 14 plants surviving out of 19 new plants, we need to find the probability of 14, 15, 16, 17, 18, and 19 plants surviving and add them up.
P(X ≥ 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19)where X is the number of new plants that survive out of 19.
From the question, the probability of any plant surviving is 0.8, therefore, the probability of any plant dying is 1 - 0.8 = 0.2.
So, the probability that exactly x plants out of 19 survive is given by: P(X = x) = \binom{19}{x}(0.8)^x(0.2)^{19 - x}
Substitute x = 14, 15, 16, 17, 18, and 19 into the above equation and sum the terms. P(X ≥ 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) = 0.2028 + 0.2857 + 0.2864 + 0.2013 + 0.0881 + 0.0229 = 0.1082
Therefore, the probability of at least 14 out of 19 plants surviving is 0.1082 (rounded to four decimal places).
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Question 5 of 10
Which pair of functions are inverses of each other?
O A. f(x) = 2 + 15 and g(x) = 12x - 15
O B. f(x) = √3x and g(x) = () ³
O c. f(x) = 3 - 10 and g(x) = +10
3
D. f(x) = 11x-4 and g(x) = +4
The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11
To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.
Let's test each option:
Option A:
f(x) = x/2 + 15
g(x) = 12x - 15
f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x
g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x
Option B:
f(x) = ∛3x
g(x) = (x/3)^3 = x^3/27
f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x
g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x
Option C:
f(x) = 3/x - 10
g(x) = (x + 10)/3
f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x
g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x
Option D:
f(x) = 11x - 4
g(x) = (x + 4)/11
f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x
g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x
Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:
D. f(x) = 11x - 4 and g(x) = (x + 4)/11
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Brynn is watching her neighbor's dogs. She earns , , but spends on Uber Eats while she is there. If she wants to earn between and dollars, how many , , must she watch the dogs. Simplify the compound inequality: 125 < 20h - 15 < 125
Answer:
Step-by-step explanation:
poop
Write an equation in slope-intercept form of the line with the given slope and y-intercepts.
slope = 0
y-intercept = 8
Answer:
The equation of the straight line y = 8
Step-by-step explanation:
Explanation:-
Given that the slope m=0 and y-intercept c=8
The equation of the straight line y=mx+c
The equation of the straight line y=0x+ 8
The equation of the straight line y = 8
No files please help me on this for math
Answer:
y=3x+8
Step-by-step explanation:
Answer:
y=1.5x+11
Step-by-step explanation:
PLEASE HELP MEE
4 thumb drives and 1 compact disk have a total capacity of 18 gigabytes. 3 compact disks and 4 thumb drives have a total capacity of 22 gigabytes. Find the capacity of 1 thumb drive (x) and the capacity of 1 compact disk (y)
The capacity of 1 thumb drive is 4 gigabytes and the capacity of 1 compact disk is 2 gigabytes.
What is the capacity of 1 thumb drive and 1 compact disk?The first step is to form the system of equations that represent the information in the question:
4x + y = 18 equation 1
4x + 3y = 22 equation 2
The elimination method would be used to determined the required values.
Subtract equation 1 from equation 2
2y = 4
y = 4/2
y = 2
Substitute for y in equation 1: 4x + 2 = 18
4x = 18 - 2
4x = 16
x = 16/4
x = 4
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The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $6.50 and each adult ticket sells for $11.50. The drama club must make a minimum of $1300 from ticket sales to cover the show's costs. Write an inequality that could represent the possible values for the number of student tickets sold, ss, and the number of adult tickets sold, aa, that would satisfy the constraint.
The inequality that could represent the possible values for the number of tickets sold will be 6.5s + 11.5a ≥ 1300.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The dramatization club is offering passes to their play to fund-raise for the show's costs. Every understudy ticket sells for $6.50 and every grown-up ticket sells for $11.50. The dramatization club should make at least $1300 from ticket deals to take care of the show's expenses.
Let 's' and 'a' be the number of tickets sold to students and adults, respectively. Then the inequality is given as,
6.5s + 11.5a ≥ 1300
The inequality that could represent the possible values for the number of tickets sold will be 6.5s + 11.5a ≥ 1300.
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calculate the distance traveled over 9hrs 45 km at a speed of 840km/h
The distance traveled over 9 hours at a speed of 840 km/h is 7,560 km.
Speed can be thought of as the rate at which an object covers distance.
A fast-moving object has a high speed and covers a relatively large distance in a given amount of time, while a slow
moving object covers a relatively small amount of distance in the same amount of time.
To calculate the distance traveled over 9 hours at a speed of 840 km/h, follow these steps:
1. Identify the time and speed given in the student question: 9 hours and 840 km/h.
2. Use the formula for distance:
distance = speed × time.
3. Plug in the values:
distance = 840 km/h × 9 hours.
4. Calculate the distance:
distance = 7,560 km.
So, the distance traveled over 9 hours at a speed of 840 km/h is 7,560 km.
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cupcakes The equation y = 2x models the cost for cookie orders from the Dotted Box Bakery, where x is number of cookies and y is cost in dollars. What is the cost per cookie?
Answer:
y=-4x+16
Step-by-step explanation:
5x+1.25=20
y=4x
5x+1.25y=20 y=4x
1.25y=-5x+20
1.25y/1.25=-5x+20/1.25
all rectangles have 2 pairs of parallel sides. all squares are rectangles with 4 congruent sides.
part 1:
do all squares have 2 pairs of parallel sides? use the statement from above to help you explain your answer
part 2:
do all rectangles have 4 congruent sides? use the statements from above to help you explain your answer
Part 1: Yes, all squares have 2 pairs of parallel sides.
Part 2: No, not all rectangles have 4 congruent sides.
Part 1: This is because all squares are rectangles, and all rectangles have 2 pairs of parallel sides. Additionally, since all four sides of a square are congruent, this means that the two pairs of sides are also congruent, making them parallel.
Part 2: While all squares are rectangles with 4 congruent sides, rectangles can have two pairs of parallel sides that are not congruent. For example, a rectangle with a length of 5 units and a width of 3 units has two pairs of parallel sides, but they are not congruent.
One pair of sides is longer than the other pair. Therefore, the fact that all squares are rectangles with 4 congruent sides does not mean that all rectangles have 4 congruent sides.
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Which of the following is a geometric sequence?
O 0, 2, 6, 12, 72,
1 2 3 4 5
2'3'4'5'6'
O4, 9, 14, 19, 24,
O
O 1, 3, 9, 27, 81,
The geometric sequence is option(D) i.e, 1, 3, 9, 27, 81,..
What is Geometric sequence ?
A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
In this, the last option have the geometric sequence. since, there is a common ration between each term. If you multiplying the previous term in the sequence by 3 gives the next term.
Hence, The geometric sequence is 1, 3, 9, 27, 81,
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Tell what each of the residual plots to the right indicates about the appropriateness of the linear model that was fit to the data. (a). Choose the best answer for residuals plot A. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases. B. The fanned pattern indicates that the linear model is not appropriate. C. The model's predicting power increases as the values of the explanatory variable increases. The scattered residuals plot indicates an appropriate linear model. (b). Choose the best answer for residuals plot A. The scattered residuals plot indicates an appropriate linear model. B. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear. C. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases.
Residual Plot A indicates that the linear model is not appropriate because the fanned pattern shows that the model's predicting power decreases as the values of the explanatory variable increases. Residual Plot B indicates that the linear model is appropriate because the scattered residuals suggest a linear relationship.
Residual Plot A shows a fanned pattern which indicates that the linear model is not appropriate. This means that the model's predicting power decreases as the values of the explanatory variable increases. This suggests that the relationship between the dependent and independent variables is not linear and a different model may be necessary. Residual Plot B, on the other hand, shows a scattered pattern which suggests that the linear model is appropriate. The scattered pattern indicates that the data points are randomly distributed, which is a sign of a linear relationship. This indicates that the linear model is an appropriate fit for the data.
the complete question is :
Tell what each of the residual plots to the right indicates about the appropriateness of the linear model that was fit to the data. (a). Choose the best answer for residuals plot A. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases. B. The fanned pattern indicates that the linear model is not appropriate. C. The model's predicting power increases as the values of the explanatory variable increases. The scattered residuals plot indicates an appropriate linear model. (b). Choose the best answer for residuals plot A. The scattered residuals plot indicates an appropriate linear model. B. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear. C. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases.
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The sun is at a focus of Earth's elliptical orbit.
a. Find the distance from the sun to the other focus.
The distance from the sun to the other focus is 5.01 × 10⁹ m.
What is the distance from the sun?
(a) The distance from the center of an ellipse to a focus is an where a is the semi major axis and e is the eccentricity. Thus, the separation of the foci ( in the case of Earth's orbit ) is;
2ae = 2(1.50 × 10¹¹)(0.0167) = 5.01 × 10⁹ m.
(b) To express this in terms of solar radii, we set up a ratio;
(5.01 × 10⁹)/(6.96 × 10⁸) = 7.2
Thus, we can conclude that the distance from the sun to the other focus is 5.01 × 10⁹ m.
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Complete question is;
The Sun's center is at one focus of Earth's orbit. How far from this focus is the other focus, (a) in meters and (b) in terms of the solar radius, 6.96 × 10⁸ m? The eccentricity is 0.0167, and the semimajor axis is 1.50 × 10¹¹ m.
math is not fun please help
Answer:
∠ RST = 22°
Step-by-step explanation:
since ∠ RSU = 91°
and ∠ TSU = 69°
so ∠ RST = 22°
HOW:
given that;
∠ RSU = 91°
and
∠ TSU = 69°
we would subtract 69° from 91°
91°-69°= 22°
The average number of students per classroom at Central High School from 2000 to 2010 can be modeled by the equation y equals 0.56 x plus 27.2., where x represents the number of years since 2000, and y represents the average number of students per classroom. Which of the following best describes the meaning of the number 0.56 in the equation?
Answer:
The estimated increase in the average number of students per classroom each year.
Step-by-step explanation:
In the equation y=0.56x+27.2, the value of x increases by 1 for each year that passes. Each time x increases by 1, y increases by 0.56, since 0.56 is the slope of the graph of this equation. Since y represents the average number of students per classroom in the year represented by x, it follows that, according to the model, the estimated increase each year in the average number of students per classroom at Central High School is 0.56.
Of the 120 rooms in a hotel, 55% are single-bed rooms, 30% are double-bedrooms, and the rest are deluxe rooms. How many deluxe rooms are there?
There are 18 deluxe rooms in the hotel.
To find the number of deluxe rooms in the hotel, we need to calculate the percentage of rooms that are deluxe.
The percentage of single-bed rooms is 55%, and the percentage of double-bedrooms is 30%. Therefore, the percentage of deluxe rooms can be calculated as:
Percentage of deluxe rooms = 100% - (Percentage of single-bed rooms + Percentage of double-bedrooms)
= 100% - (55% + 30%)
= 100% - 85%
= 15%
So, 15% of the total rooms in the hotel are deluxe rooms.
To determine the number of deluxe rooms, we can multiply the total number of rooms by the percentage of deluxe rooms:
Number of deluxe rooms = 15% of 120 rooms
= (15/100) * 120
= 0.15 * 120
= 18
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Jorge has 18 fish for his dog sled team that he wants to divide into smaller pieces. How many pieces of fish would there be if Jorge divided each fish into tenths?
0.18
1.8
180
1,800
The number of pieces of fish Jorge would have if Jorge divided each fish into tenths is 180 fishes.
The correct answer option is option C
How to divide the fishes in his dog sled team?Division is the process of separating into various parts. It is represented by the symbol ÷ or /
Number of fishes Jorge has = 18NumberJorge divided each fish into = tenths = 0.1Number of fishes Jorge would have = Number of fishes Jorge has / NumberJorge divided each fish into
= 18 / 0.1
= 180 fishes
In conclusion, the total number of fishes Jorge would have after division is 180 fishes.
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The HCF of 85 and 95
Answer:
So the greatest common factor 85 and 95 is 5.
Step-by-step explanation:
We will now calculate the prime factors of 85 and 95, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85 and 95.
We will first find the prime factorization of 85 and 95. After we will calculate the factors of 85 and 95 and find the biggest common factor number .
Step-1: Prime Factorization of 85Prime factors of 85 are 5, 17. Prime factorization of 85 in exponential form is:
85 = 5^1 × 17^1
Step-2: Prime Factorization of 95Prime factors of 95 are 5, 19. Prime factorization of 95 in exponential form is:
95 = 5^1 × 19^1
Step-3: Factors of 85List of positive integer factors of 85 that divides 85 without a remainder.
1, 5, 17
Final Step: Biggest Common Factor NumberWe found the factors and prime factorization of 85 and 95. The biggest common factor number is the GCF number.
So the greatest common factor 85 and 95 is 5.
What is the vertex form of each function?
a. y = x^2 - 2x + 3
b. y = x^2 + 6x + 25
please answer quickly-
PLS HELP ASAP 100 POINTS
Find the measure of ∠YOZ by answering the questions.
1. Find the measure of ∠WOV. Which angle relationship did you use? (3 points)
2. Now find the measure of ∠YOZ. Which angle relationship did you use?
3. Check your answer by using another strategy to find the measure of ∠YOZ. Describe your strategy, and show that it gives the same measure for ∠YOZ. (4 points)
Answer:
60°60°, vertical angles60°, measure of a straight angleStep-by-step explanation:
Given right angle XOV and 30° angle XOW, you want to know the measure of angle WOV. You also want to find the measure of angle YOZ, which is opposite angle VOW, where XOY is a right angle, and WOZ is a straight angle.
1. WOVThe angle addition theorem tells you that ...
∠XOW +∠WOV = ∠XOV
Angle XOV is given as a right angle, and angle XOW is shown as 30°, so we have ...
30° +∠WOV = 90°
∠WOV = 60° . . . . . . . . . subtract 30° from both sides
Angle WOV is 60° using the angle addition theorem.
2. YOZRays OY and OV are opposite rays, as are rays OZ and OW. This means angles YOZ and VOW are vertical angles, hence congruent.
∠YOZ = ∠WOV = 60°
Angle YOZ is 60° using the congruence of vertical angles.
3. YOZ another wayAs in part 2, angle WOZ is a straight angle, so measures 180°. The angle addition theorem tells you this is the sum of its parts:
∠ZOY +∠YOX +∠XOW = ∠ZOW
∠ZOY +90° +30° = 180°
∠ZOY = 60° . . . . . . . . . . . . . subtract 120° from both sides
Angle YOZ is 60° using the measure of a straight angle.
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Suppose you have an outdoor vegetable garden with dimensions 2 mx2 m. A storm lasting 1 hr delivers 0.8 inches of rain. a. What is the storm rainfall flux? Express your answer using each of the following units: m 2
hr
kgliquid water m 2
hr
lb liquid water m 2
hr
liters liquid water m 2
hr
gallons liquid water b. How much liquid water fell on your garden? Express your answer using each of the following units:
The storm rainfall flux is 0.00127 m2/hr, 1.27 kg liquid water/m2hr, 2.8 lb liquid water/m2hr, 1.27 liters liquid water/m2hr, and 0.335 gallons liquid water/m2hr. The amount of liquid water fell on the garden is 80.6 L, 21.3 gallons.
Dimensions of outdoor vegetable garden = 2 m × 2 m
Storm rainfall = 0.8 inches of rain
Time of storm = 1 hr(
a) The rainfall flux is the amount of rainfall per unit area and unit time. It is given as:
Rainfall flux = (Amount of rainfall) / (Area × Time)
Given the area of the garden is 2 m × 2 m, and the time is 1 hr, the rainfall flux is:
Rainfall flux = (0.8 inches of rain) / (2 m × 2 m × 1 hr)
Converting inches to meters, we get:
1 inch = 0.0254 m
Therefore,
Rainfall flux = (0.8 × 0.0254 m) / (2 m × 2 m × 1 hr) = 0.00127 m/hr
Converting the rainfall flux to other units:
In kg/hr:
1 kg of water = 1000 g of water
Density of water = 1000 kg/m3
So, 1 m3 of water = 1000 kg of water
So, 1 m2 of water of depth 1 m = 1000 kg of water
Therefore, 1 m2 of water of depth 1 mm = 1 kg of water
Therefore, the rainfall flux in kg/hr = (0.00127 m/hr) × (1000 kg/m3) = 1.27 kg/m2hr
In lbs/hr:
1 lb of water = 453.592 g of water
So, the rainfall flux in lbs/hr = (0.00127 m/hr) × (1000 kg/m3) × (2.20462 lb/kg) = 2.8 lbs/m2hr
In liters/hr:
1 m3 of water = 1000 L of water
So, 1 m2 of water of depth 1 mm = 1 L of water
Therefore, the rainfall flux in L/hr = (0.00127 m/hr) × (1000 L/m3) = 1.27 L/m2hr
In gallons/hr:
1 gallon = 3.78541 L
So, the rainfall flux in gallons/hr = (0.00127 m/hr) × (1000 L/m3) × (1 gallon/3.78541 L) = 0.335 gallons/m2hr
(b) To calculate the amount of water that fell on the garden, we need to calculate the volume of water.
Volume = Area × Depth.
The area of the garden is 2 m × 2 m.
We need to convert the rainfall amount to meters.
1 inch = 0.0254 m
Therefore, 0.8 inches of rain = 0.8 × 0.0254 m = 0.02032 m
Volume of water = Area × Depth = (2 m × 2 m) × 0.02032 m = 0.0806 m3
Converting the volume to other units:
In liters:
1 m3 of water = 1000 L of water
Therefore, the volume of water in liters = 0.0806 m3 × 1000 L/m3 = 80.6 L
In gallons:
1 gallon = 3.78541 L
Therefore, the volume of water in gallons = 80.6 L / 3.78541 L/gallon = 21.3 gallons.
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Finding trigonometric ratios:
( ONLY QUESTIONS 10, 12 and 14)
Step-by-step explanation:
Sorry that they're sideways, it's the only way brainy would let me send them!!
Huilan is 15 years older than Thomas. The sum of their ages is 115 . What is Thomas's age?
Answer:
50
Step-by-step explanation:
undo in reverse order
subtract 15 from 115 and divide the answer in half
hope this helps!
Answer:
Step-by-step explanation:
Huilan is 15 years older than Thomas. The sum of their ages is 115 . What is Thomas's age?
115 - 15 = 100
100 : 2 = 50 (huilan)
50 + 15 = 65 (Thomas)
-----------------------
50 + 65 = 115
65 - 50 = 15
the answer is good
Is the following statement true or false? Explain your reasoning. 3 + 2 = 6 or 9 – 2 = 7
Answer:
true : 9-2=7 false:3+2=6
Step-by-step explanation:
the first equation is false because if you take 6 and minus 3 you get three not two, But with the other equation its diffrent you take 7 and add it to two you get nine.
What are the domain and range of the function
Answer:
Domain (-∞,∞)
Range (0, ∞)
Step-by-step explanation:
The domain of a function is always the set of all real numbers therefore the domain is going to be (-∞,∞). The range is (0, ∞) because 0 is one of the outputs for the function
Help ASAP!!!!!!!!!!!!!!!!
The correct order of match is 1-a, 2-b, 3-d and 4-c.
What are conic sections?The term "conic" refers to a curve formed by the intersection of a right circular cone with a plane. In Euclidean geometry, it has distinctive features. The cone is split into two nappes, the upper nappe and the lower nappe, at its vertex.
A plane crosses the cone, and the resulting section is referred to as a conic section.
Given the equations,
the equation for parabola is given by
(y - b)² = 4p(x - a)
Vertex is (a,b)
equation 2 follows the same
x = -2(y - 4)² + 3
this is the equation for parabola.
Equation for ellipse is
(x − a)²/h² + (y − b)²/k² = 1
the equation x²/4 + (y - 8)²/144 = 1
(x/2)² + ((y - 8)/12)² = 1
the equation is same is equation for ellipse,
Equation for circle
(x - h)² + (y - k)² = r²
fourth equation
(x - 9)² + (y + 2)² = 7²
is same as equation of circle
Equation for hyperbola
(x − a)²/h² − (y − b)²/k² = 1
equation (x - 3)²/5 - (y + 4)²/25 = 1
is same as equation of hyperbola.
Hence the correct order is a, b, d, and c.
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