Answer:
Mother: £200, Sister: £80, Mary: £120
Step-by-step explanation:
Mary has a total of £400 to start off with.
In order to calculate the amount she gives to her mother, we must multiply 400 by .5 (the decimal equivalent of 50%), which leaves us with £200 to her mother.
Do the same with her sister; multiply 400 by .2 (the decimal equivalent of 20%), which leaves us with £80.
To figure out what she is left with, £400 - 200 - 80 = £120. Mary is left with £120.
Mary will have £120 with her, her mother will have £200 and her sister will have £80.
What is percentage?Percentages are fractions with 100 as the denominator. It is the relation between part and whole where the value of whole is always taken as 100.
Given that, Mary won £400.
She gave 50% to her mother, 20% to her sister and rest she kept with herself,
So,
The amount her mother got =
50% of £400 = 1/2 × 400 = 200
Therefore, her mother got £200.
The amount her sister got =
20% of £400 = 1/5 × 400 = 80
Therefore, her sister got £80.
The amount Mary have = 400 - (200+80) = 400 - 280 = £120
Hence Mary will have £120 with her.
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Answer this
………………..
The slope of the linear equation is; 0.5
The y-intercept of the Linear Equation is: 4.75
Yes the equation is proportional
What is the graph of the linear Equation?The equation we are given is expressed as;
y = ¹/₂x + 4³/₄
When x = 0,
y = ¹/₂(0) + 4³/₄
y = 4.75
When x = 1,
y = ¹/₂(1) + 4³/₄
y = 5.25
When x = 2,
y = ¹/₂(2) + 4³/₄
y = 5.75
When x = 3,
y = ¹/₂(3) + 4³/₄
y = 6.25
If we go on and on till x = 10, we will see the constant difference in y for every change in x is 0.5
Thus, slope = 0.5
y-intercept = 4.75
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what is the answer to this question?
Answer:
Dude.....it's a CIRCLE!!
# 20 i
STRUCTURE Find the value of x for which PQ|| RS
P 2x + 4
Q
x =
3x + 5
Previous
13
R
14
S5
7
15
T
16
The value of the variable x for the similar triangles is equal to 3
How to evaluate the value of x for the similar trianglesThe triangles PTQ and STR are similar, this implies that the length ST of the smaller triangle is similar to the length PT of the larger triangle
and the length RT of the smaller triangle is similar to the length QT of the larger triangle
so;
5/(2x + 9) = 7/(3x + 12)
5(3x + 12) = 7(2x + 9) {cross multiplication}
15x + 60 = 14x + 63
15x - 14x = 63 - 60 {collect like terms}
x = 3.
Therefore, the value of the variable x for the similar triangles is equal to 3
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Two groups of hikers leave the same camp heading in opposite directions. The first group travels 2 miles north & 5 miles east. The second group travels 3 miles south and 7 miles west.
The distance between the two groups after the hikes is approximately 12.04 miles.
The Pythagorean Theorem: What is it?A right triangle's connection between its sides is described by the Pythagorean Theorem, a foundational idea in mathematics. It claims that the hypotenuse's square length, which is the side that faces the right angle, equals the sum of the squares of the lengths of the other two sides of any right triangle. The Pythagorean Theorem is frequently used to solve issues involving distance, velocity, and acceleration and has various applications in the disciplines of geometry, trigonometry, and physics.
The distance between the two groups serves as the hypotenuse of a right triangle, which is formed by the two pathways. The following formula can be used to determine the hypotenuse's length:
Distance = √((2+7)² + (5+3)²)
= √(9² + 8²)
= √(81 + 64)
= √(145)
≈ 12.04 miles
Therefore, the distance between the two groups after the hikes is approximately 12.04 miles.
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50 points
dias older brother likes his hot chocolate made with 2 ounces of cocoa and 3 ounces of milk. Whose how chocolate is more chocolaty
Dina likes hers with 3 ounces of chocolate and 5 ounces of milk
Explains how u got the answer
Dina's older brother has a hot chocolate that is more chocolaty, as his recipe has a higher proportion of cocoa.
How to define which is the more chocolaty recipe?The more chocolaty recipe is defined obtain the proportion of cocoa for each recipe.
The proportion of cocoa for each recipe is obtained dividing the amount of cocoa used by the sum of the amounts of cocoa and milk used.
Hence the proportion for Dina's older brother is calculated as follows:
2/(2 + 3) = 2/5 = 0.4 = 40% cocoa.
The proportion for Dina's is obtained as follows:
3/(3 + 5) = 3/8 = 0.375 = 37.5% cocoa.
40 > 37.5, hence Dina's older brother has a hot chocolate that is more chocolaty, as his recipe has a higher proportion of cocoa.
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Emmett is planning a party at an escape room. The escape room will charge Emmett a booking fee and an additional cost per person attending the party.
This situation can be modeled as a linear relationship.
Emmett is planning a party at an escape room. The escape room will charge Emmett a booking fee and an additional cost per person attending the party.
This situation can be modeled as a linear relationship.
What does the slope of the line tell you about the situation?
A. The booking fee is $50
B. After the booking fee the party will cost $20 per person
C. After the booking fee the party will cost $25 per person
D. Including the bookin fee it would cost emmett $250 total for 10 people to attend
The provide situation can be modeled as a linear equation, y = 50 + 20x, where y is total cost and x is number of person who will attend the party. The slope of line tells me that the additional cost per person attending the party is $20. Thus, write option is option (b).
Emmett wants to through a party at an escape room. There are two charges for
escape room, one is booking fee and other one is additional cost per person attending the party. Let the booking fee and additional cost per person who attended the party of escape room be 'a ' and 'b'. Also, consider total person who will attend the party are equal to 'x'. So, total cost = booking cost + additional cost per person × number of people's who will attend the party. Let total cost of escape room for x people be 'y'. Then,
y = a + bx --(1)
it is act as modeled linear relationship, see above graph, which represents it graphically. In the graph initial total cost is 50, when no additional cost occur, that is booking fee equals to $50 or a = $50. After that, number of people increase total cost also increases. When there are 10 people in party then total cost is $250 and the additional cost = $200 for 10 people. So, additional cost per person
= 200/10 = 20 , i.e., b = $20 and equation(1) is rewrite, y = 50 + 20x.
If we compare it with standard linear equation, y = mx + c
where m --> slope of line
c --> y-intercept
then slope of equation (1) is equals to 'b' and b = 20. In this situation, the slope of line tell me that except the booking fee, the additional cost per person who will attend the party is equals to $20. Hence, the required answer is option(b).
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Complete question:
Emmett is planning a party at an escape room. The escape room will charge Emmett a booking fee and an additional cost per person attending the party.
This situation can be modeled as a linear relationship, see above graph. What does the slope of the line tell you about the situation?
A. The booking fee is $50
B. After the booking fee the party will cost $20 per person
C. After the booking fee the party will cost $25 per person
D. Including the bookin fee it would cost emmett $250 total for 10 people to attend.
B. After the booking fee the party will cost $20 per person
According to a research institution, men spent an average of $134.71 on Valentine's Day gifts in 2009. Assume the standard deviation for this population is $30 and that it is normally distributed. A random sample of 10 men who celebrate Valentine's Day was selected. Complete parts a through e.
a. Calculate the standard error of the mean.
b. What is the probability that the sample mean will be less than $125?
c. What is the probability that the sample mean will be more than $145?
d. What is the probability that the sample mean will be between $120 and $160?
e. Identify the symmetrical interval that includes 95% of the sample means if the true population mean is $134.71.
a. The standard error of the mean would be 9.49.
b. The probability that the sample mean will be less than $125 is 0.1539.
c. The probability that the sample mean will be more than $145 is 0.1401.
d. The probability that the sample mean will be between $120 and $160 is 0.9356.
e. The symmetrical interval that includes 95% of the sample means is ($116.11, $153.31).
a. The standard error of the mean is calculated using the formula:
SE = σ / √n
where σ is the standard deviation and n is the sample size.
In this case, σ = $30 and n = 10. So, the standard error of the mean is:
SE = 30 / √10
SE = 9.49
b. To find the probability that the sample mean will be less than $125, we need to calculate the z-score:
z = (x - μ) / SE
where x is the sample mean, μ is the population mean, and SE is the standard error of the mean.
In this case, x = $125, μ = $134.71, and SE = 9.49. So, the z-score is:
z = (125 - 134.71) / 9.49
z = -1.02
Using a z-table, we find that the probability of getting a z-score less than -1.02 is 0.1539. So, the probability that the sample mean will be less than $125 is 0.1539.
c. To find the probability that the sample mean will be more than $145, we need to calculate the z-score:
z = (x - μ) / SE
where x is the sample mean, μ is the population mean, and SE is the standard error of the mean.
In this case, x = $145, μ = $134.71, and SE = 9.49. So, the z-score is:
z = (145 - 134.71) / 9.49
z = 1.08
Using a z-table, we find that the probability of getting a z-score less than 1.08 is 0.8599. So, the probability that the sample mean will be more than $145 is 1 - 0.8599 = 0.1401.
d. To find the probability that the sample mean will be between $120 and $160, we need to calculate the z-scores for both values:
z1 = (x1 - μ) / SE
z2 = (x2 - μ) / SE
where x1 and x2 are the sample means, μ is the population mean, and SE is the standard error of the mean.
In this case, x1 = $120, x2 = $160, μ = $134.71, and SE = 9.49. So, the z-scores are:
z1 = (120 - 134.71) / 9.49
z1 = -1.55
z2 = (160 - 134.71) / 9.49
z2 = 2.67
Using a z-table, we find that the probability of getting a z-score less than -1.55 is 0.0606 and the probability of getting a z-score less than 2.67 is 0.9962. So, the probability that the sample mean will be between $120 and $160 is 0.9962 - 0.0606 = 0.9356.
e. To find the symmetrical interval that includes 95% of the sample means, we need to use the formula:
x = μ ± z*SE
where x is the sample mean, μ is the population mean, z is the z-score, and SE is the standard error of the mean.
In this case, μ = $134.71, z = 1.96 (for a 95% confidence interval), and SE = 9.49. So, the symmetrical interval is:
x = 134.71 ± 1.96*9.49
x = 134.71 ± 18.6
x = (116.11, 153.31)
So, the symmetrical interval that includes 95% of the sample means is ($116.11, $153.31).
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Determine the values for which the rational expression is undefined. ((8x)/(z)) x=z
The rational expression is undefined when the denominator is equal to zero. This is because division by zero is not allowed in mathematics, and the result would be "undefined."
To find the values for which the rational expression is undefined, we need to set the denominator equal to zero and solve for the variable. In this case, the denominator is z:
z = 0
Therefore, the rational expression is undefined when z = 0.
So, the values for which the rational expression ((8x)/(z)) is undefined are:
z = 0
I hope this helps! Let me know if you have any further questions.
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Which of the following expressions is equivalent to -2(-x^2-3)
A. 2x^2-6
B. 2x^2-3
C. 2x^2*3
D. 2x^2+6
Answer:
2(−x 2−3)
Simplify the expression
−2x 2−6
Factor the expression
−2(x 2+3)
Nicole has 15 nickels and dimes. If the value of her coins is $
1.10how many of each coin does she have?
Nicole has 8 nickels and 7 dimes.
What is system of equations?A system of equations is simply two or more equations that share the same variables.
Let's use a system of equations to solve this problem:
Let x be the number of nickels, and y be the number of dimes.
From the problem, we know that:
x + y = 15 (equation 1) (the total number of coins is 15)
0.05x + 0.1y = 1.1 (equation 2) (the total value of the coins is $1.10)
To solve for x and y, we can use substitution or elimination. Let's use elimination:
Multiply equation 1 by 0.1:
0.1x + 0.1y = 1.5 (equation 3)
Subtract equation 3 from equation 2:
0.05x = 0.4
x = 8
Substitute x = 8 into equation 1:
8 + y = 15
y = 7
Therefore, Nicole has 8 nickels and 7 dimes.
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Hudson was making $9.00 per hour before his raise. He is now making $9.45 per hour. what is his increase pay ?
Answer:
$0.45
Step-by-step explanation:
y=-3x-7 y=x+9 solve by substitution how do I do this, I'm so lost!
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Answer:
Point Form:
(−8,−17)
Equation Form: x=−8,y=−17
Answer:
x=-4, y=5
Step-by-step explanation:
Because y=-3x-7 and y=x+9, so y=y, and -3x-7=x+9
-3x-7=x+9,
so 4x=-16
x=-4
so we put x=-4 to y=-3x-7
y=(-3)* (-4)-7
y=12-7
y=5
Which condition will not create a gap or an overlap at a vertex of polygons?
The sum of the measures of the angles is greater than 360°.
The sum of the measures of the angles is equal to 360°.
The sum of the measures of the angles is less than 360°.
When the sum of the angles is exactly 360 degrees, there is no overlap or gap at the vertex.
What is a polygon ?
A polygon is a two-dimensional closed shape made up of line segments. It has three or more straight sides and angles. Some common examples of polygons are triangles, rectangles, squares, pentagons, hexagons, and octagons.
The properties of a polygon, such as the number of sides, angles, and vertices, depend on its type and shape.
The condition that will not create a gap or an overlap at a vertex of polygons is "The sum of the measures of the angles is equal to 360°."
When the sum of the angles is exactly 360 degrees, there is no overlap or gap at the vertex.
This condition is also known as the angle sum property of polygons, and it states that the sum of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees.
Therefore, When the sum of the angles is exactly 360 degrees, there is no overlap or gap at the vertex.
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Graduate Management Admission Test (GMAT) is a computer adaptive test intended to assess certain analytical, writing, quantitative, verbal and reading skills in written English for use in admission to a graduate management program such as an MBA programme. GMAT scores are normally distributed with a mean of 550 and a standard deviation of 120. Suppose a random sample of 35 students is selected randomly. (a) Describe the shape of the sampling distribution of the sample means. State the theorem used and explain briefly. (b) Find the mean and the standard deviation of the sample means. (c) What is the probability that the average score of those 35 selected students is above 600? (d) A student, Ann, is randomly selected from the population, find the probability that her score is above 600?
The probability that Ann's score is above 600 is 1 - 0.6628 = 0.3372.
(a) The shape of the sampling distribution of the sample means will be approximately normal. This is because of the Central Limit Theorem, which states that the sampling distribution of the sample means will be approximately normal if the sample size is large enough, regardless of the shape of the population distribution. In this case, the sample size of 35 is large enough for the Central Limit Theorem to apply.
(b) The mean of the sampling distribution of the sample means will be equal to the mean of the population, which is 550. The standard deviation of the sampling distribution of the sample means will be equal to the standard deviation of the population divided by the square root of the sample size, which is 120/√35 ≈ 20.28.
(c) To find the probability that the average score of the 35 selected students is above 600, we need to find the z-score for 600 using the mean and standard deviation of the sampling distribution of the sample means. The z-score is (600 - 550)/20.28 ≈ 2.47. Using a z-table, we can find the probability that the z-score is less than 2.47, which is 0.9932. Therefore, the probability that the average score of the 35 selected students is above 600 is 1 - 0.9932 = 0.0068.
(d) To find the probability that Ann's score is above 600, we need to find the z-score for 600 using the mean and standard deviation of the population. The z-score is (600 - 550)/120 ≈ 0.42. Using a z-table, we can find the probability that the z-score is less than 0.42, which is 0.6628.
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Instructions Use this triangle for problems 1-3
1. what is the value of angle B?
2. What is the length of BC
3. What is the length of AB
Answer:
Q1 Value of angle B = 50°
Q2 BC = 1.3
Q3 AB = 2.57
Step-by-step explanation:
For Part 1
The three angles of a triangle must add up to 180°
Therefore m∠B + 30 + 100 = 180
m∠B + 130 = 180
m∠B = 180 - 30 = 50°
part 2
The law of sines states that, in a triangle, the ratio of each side to the sine of the angle opposite that side must be the same for all sides
We have side AC opposite ∠B
AC = 2 and we found that m∠B = 50° from part 1
The side BC is opposite ∠A which is 30°
Therefore, applying the law of sines
[tex]\dfrac{{AC}}{\sin 50^\circ} = \dfrac{{BC}}{\sin 30^\circ}\\\\\\\dfrac{2}{\sin 50^\circ} = \dfrac{{BC}}{\sin 30^\circ}\\\\[/tex]
Multiplying both sides by sin 30° we get
[tex]\dfrac{2}{\sin 50^\circ} \times \sin 30^\circ =BC\\\\or\\\\BC = \dfrac{2}{\sin 50^\circ} \times \sin 30^\circ[/tex]
Using a calculator to compute the right side we get
BC = 1.30540 ≈ 1.3
part 3
Similarly
[tex]\dfrac{AB}{\sin 100} = \dfrac{2}{\sin50}\\\\AB = \sin 100 \times \dfrac{2}{\sin 50} = 2.57115 \approx 2.57[/tex]
In the equation T = 30 - 5h, the y-intercept is
and the coefficient is
Answer: The y-intercept is 30 and the coefficient is -5
Step-by-step explanation:
In the slope-intercept form (y = mx + b) b stands for your y-intercept, in this case, 30.
The coefficient is the number being multiplied by the variable, or in this case, the slope, or -5.
Chen needs an average of 80% or greater on her test scores to earn a B in math class for the quarter. Each test is worth 50 points. The scores of her first three tests are shown in the table. There is one more test this quarter.
In a linear equation, There is one more test this quarter 39.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
lowest average score = 80% * 50 = 40
suppose the final exam score she must get at least x.
( x + 45 + 38 + 36) = 4 ≥ 40
x ≥ 39
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What are the coordinates of point D (3/4,3)
after it is reflected across the x-axis?
When a point is reflected across the x-axis, its y-coordinate changes sign while its x-coordinate remains the same.
Therefore, to find the coordinates of the reflected point D, we simply change the sign of the y-coordinate of point D.
Given that the coordinates of point D are (3/4,3), its reflected point D' across the x-axis will have the coordinates (3/4, -3).
Therefore, the reflected point D' is located at the point (3/4, -3).
Coordinates are pairs of numbers used to identify the position of a point in a two-dimensional plane. In a Cartesian coordinate system, the two numbers represent the x-coordinate (the horizontal position) and the y-coordinate (the vertical position) of the point.
For example, the point (3, 5) has an x-coordinate of 3 and a y-coordinate of 5. This means that the point is located 3 units to the right of the origin (the point where the x- and y-axes intersect) and 5 units above the x-axis. Similarly, the point (-2, -1) has an x-coordinate of -2 and a y-coordinate of -1, which means that it is located 2 units to the left of the origin and 1 unit below the x-axis.
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Two cheeseburgers and one small order of fries contain a total of 1420 calories. Three cheeseburgers and two small orders of fries contain a total of 2290 calories. Find the caloric content of each item.
One cheeseburgers have 550 Cal and on smalls Fries have 320 Cal.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Two cheeseburgers and one small order of fries contain a total of 1420 calories.
Three cheeseburgers and two small orders of fries contain a total of 2290 calories.
let the number of Calories in one cheeseburgers be x and in one fries be y.
So, the system of Equation is:
2x + y = 1420
3x + 2y= 2290
solving the above two equation
x= 550 and y= 320
So, one cheeseburgers have 550 Cal and on smalls Fries have 320 Cal.
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The expression - 16x + 24x + 4.2 represents the height of a ball, in feet, × seconds after it is thrown. What does 4.2 represent in this context?
Answer:
4.2 represents the initial height of the ball.
Step-by-step explanation:
h(x) = -16x² + 24x + 4.2
At x = 0, h(0) = 4.2
4.2 represents the initial height of the ball.
Student Edition. Geometry. Volume 2 < 75 of 350---> 5. BLUEPRINTS Ezra is redrawing the blueprint shown of a stage he is planning to build for his band. By what percentage should he multiply the dimensions of the stage so that the dimensions of the image are the size of the original blueprint? What will be the perimeter of the updated blueprint? (Example 2) 10 units 4 units 8 units Long Description 10 units 2 units
Ezra should increase the stage's dimensions by the following factor in order to make the picture half the size of the original blueprint:
50%.
The modified blueprint will have a perimeter that is half that of the original layout.
What is a dilation?When the scale factor is multiplied by the coordinates of an image's vertices, the result is a dilatation, which alters the side lengths of a figure.
The scale factor of the dilation is supplied as follows because, for this issue, we want the updated stage's dimensions to be half those of the original stage.
k = 1/2.
Given that both the perimeter and the side lengths have the same unit, 50%, or half of the original stage's perimeter, will be represented by the updated stage's perimeter.
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Zach has already saved 2/3 of the money he will need for his trip. From this month's paycheck, he plans to put aside 3/4 of what he has left to save. how much of the total amount does Zach still have to save after this month?
Zach still has to save 1/12 of the total amount after this month.
To find out how much of the total amount Zach still has to save after this month, we need to calculate how much he has already saved and how much he will save from this month's paycheck.
First, we know that Zach has already saved 2/3 of the money he will need for his trip. So, if we let x be the total amount he needs for the trip, we can write this as:
Already saved = 2/3 * x
Next, we know that Zach plans to put aside 3/4 of what he has left to save from this month's paycheck. Since he has already saved 2/3 of the total amount, he has 1/3 of the total amount left to save. So, the amount he will save from this month's paycheck is:
Amount from paycheck = 3/4 * (1/3 * x) = 1/4 * x
Now, we can add these two amounts to find out how much Zach has saved in total:
Total saved = Already saved + Amount from paycheck
Total saved = (2/3 * x) + (1/4 * x) = (8/12 * x) + (3/12 * x) = 11/12 * x
Finally, we can subtract this amount from the total amount he needs to find out how much he still has to save:
Amount still to save = Total amount - Total saved
Amount still to save = x - (11/12 * x) = (12/12 * x) - (11/12 * x) = 1/12 * x
So, Zach still has to save 1/12 of the total amount after this month.
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select the number line that shows that two oppsite numbers have the sum of 0
Answer: I'd say A
Step-by-step explanation:
-1+1=0
Bright Designs Crayon Factory uses 400 milliliters of melted wax for each of their crayons. The factory puts 16 crayons in each box and produces 500 boxes of crayons each day. How many liters of melted wax does Bright Designs Crayon Factory use each day?
Answer:
First, let's find the total number of crayons produced each day:
500 boxes/day x 16 crayons/box = 8,000 crayons/day
Since each crayon uses 400 milliliters of melted wax, the total amount of wax used in one day can be found by multiplying the number of crayons by the amount of wax used per crayon and converting from milliliters to liters:
8,000 crayons/day x 400 mL/crayon x 1 L/1000 mL = 3,200 liters/day
Therefore, Bright Designs Crayon Factory uses 3,200 liters of melted wax each day.
Step-by-step explanation:
Answer:
Bright Designs Crayon Factory uses 3,200 liters of melted wax each day.
Step-by-step explanation:
What is the set builder equation for
x y
1/125 -3
1/25 -2
1/5 -1
1 0
5 1
25 2
125 3
The set builder nοtatiοn wοuld be {(x, y) | x = 1/125, 1/25, 1/5, 1, 5, 25, 125 and y = -3, -2, -1, 0, 1, 2, 3}
What is a set builder equatiοn?A set builder nοtatiοn is a cοncise way οf representing a set οf elements based οn a rule οr cοnditiοn. In set builder nοtatiοn, we use braces { } tο enclοse the set οf elements, and a vertical bar | οr a cοlοn : tο separate the cοnditiοn frοm the elements. The general fοrmat οf a set builder nοtatiοn is:
{elements | cοnditiοn}
Using this nοtatiοn, we can represent the set οf οrdered pairs (x, y) given in the questiοn as:
{(x, y) | x = 1/125, 1/25, 1/5, 1, 5, 25, 125 and y = -3, -2, -1, 0, 1, 2, 3}
This nοtatiοn reads as "the set οf all οrdered pairs (x, y) such that x takes οn the values 1/125, 1/25, 1/5, 1, 5, 25, and 125, and y takes οn the values -3, -2, -1, 0, 1, 2, and 3."
Hence, the set builder nοtatiοn wοuld be {(x, y) | x = 1/125, 1/25, 1/5, 1, 5, 25, 125 and y = -3, -2, -1, 0, 1, 2, 3}
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the given binomial a factor of the given polynomial? If so, write the polynomial: P(x)=2x^(3)+3x^(2)-2x-3; binomial: 2x+3
Yes, the binomial 2x+3 is a factor of the given polynomial P(x)=2x^(3)+3x^(2)-2x-3. We can verify this by using synthetic division.
First, we need to find the zero of the binomial, which is -3/2. Then, we can use synthetic division to divide the polynomial by the binomial.
Here are the steps for synthetic division:
1. Write the coefficients of the polynomial in a row: 2 3 -2 -3
2. Write the zero of the binomial to the left of the row: -3/2 | 2 3 -2 -3
3. Bring down the first coefficient: -3/2 | 2 3 -2 -3
0 -3 6 -6
---------------
2 0 4 -9
4. Multiply the zero by the first coefficient and write the result below the second coefficient: -3/2 * 2 = -3
5. Add the second coefficient and the result: 3 + (-3) = 0
6. Repeat steps 4 and 5 for the remaining coefficients: -3/2 * 0 = 0, -2 + 0 = -2; -3/2 * -2 = 3, -3 + 3 = 0
7. The final row of numbers represents the coefficients of the quotient: 2x^(2) + 0x + 4, with a remainder of -9.
Since the remainder is not zero, the binomial is not a factor of the polynomial. However, if we divide the polynomial by the binomial using long division, we get the following:
2x^(2) + 4 - (9/(2x+3))
This means that the polynomial can be written as: P(x) = (2x+3)(2x^(2) + 4) - 9
So, the binomial 2x+3 is a factor of the polynomial P(x)=2x^(3)+3x^(2)-2x-3.
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For each equation in the table below, determine if the equation represents exponential growth or exponential decay. Select Growth or Decay for each equation.
Growth Decay
Equation
1. y = 500(0.30) G or D?
2. y = 500(1.70) G or D?
3. y = 0.3(500) G or D?
3. y=500(0.30) - 6 G or D?
4.y = 0.3(1.7)¹-2 G or D?
5. y = 500(0.30)+2 G or D?
6. y = 500(0.30)-6 G or D?
The expression are classified as follows
1. Decay
2. Growth
3. Growth
3. Decay
4. Growth
5. Decay
6. Decay
How to determine growth or decay functionExponential function refers to functions of the form
f(x) = a(b)^x
where
the starting = a
the base = b
the exponents = x
The base is what determines exponential growth or decay
when the base is greater than 1 we have exponential growth
when the base is 0 < x < 1 we have exponential decay
comparing the base of the functions shows that
1. y = 500(0.30) decay
2. y = 500(1.70) growth
3. y = 0.3(500) growth
3. y=500(0.30) - 6 decay
4.y = 0.3(1.7)¹-2 growth
5. y = 500(0.30)+2 decay
6. y = 500(0.30)-6 decay
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Of the 34 cars in a parking lot, 20 are green, 8 are gold, and the rest are black. What are the odds against the next car leaving the lot being black?
A. 3:14
B. 3:28
C. 28:3
D. 14:3
This spinner has 6 equal sections. In simplest form, what are the odds in favor of spinning blue or green?
A. 1:2
B. 1:3
C. 3:1
D. 2:1
What are the odds against getting three tails when you flip three coins?
A. 1:1
B. 1:7
C. 1:8
D. 7:1
(You can do one answer if u want explaination would be helpful)
The odds against the next car leaving the lot being black = option(A) is correct option.
The odds against getting three tails when you flip three coins = option(B) is the correct option.
What is probability?
The potential of any random event's result is referred to as probability. To determine the likelihood that any event will occur is the definition of this phrase.
There 34 cars out of which 20 are green, 8 are gold and 6 are black.
So, The odds against the next car leaving the lot being black
= no. of black cars / no. of non black cars
= 6/28
=3/14 (A)
If three coins are flipped together,
the total number of outcomes will be = 2³ = 8
no. of outcomes getting three tails = 1
The odds against getting three tails when you flip three coins
= no. of outcomes getting three tails/ no. of outcomes not getting three tails
= 1/7 (option B)
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Function g is a transformation of f(x) = 2x. Compare the graphs of the functions. Select all that apply.
x= 1 2 3 4 5
g(x)= 1/8 1/4 1/2 1 2
In response to the query, we have that The two graphs are oriented and coordinates have the same form in common. The moment where the two graphs come together (1, 2).
what are coordinates?A coordinate system is a technique used in geometry to precisely locate points or other geometry objects on a manifold, also including Euclidean space, using one or more numbers or coordinates. A point or item on a two-dimensional sphere is located using a pair of numbers known as coordinates. The x and y positions are two numbers that describe a point's location on a 2D plane. a collection of integers that indicate exact locations. Typically, the figure has two numbers. The first number represents the front-to-back distance, while the second column represents the top-to-bottom distance. When there are 12 units below and 5 above, as in (12.5), this is an example.
f(1/x) = 2/(1/x) = 2x, where g(x) =
Hence, g(x) = f(1/x) is equivalent to f(x) = 2x.
The values of x and g(x) are as follows:
x= 1 2 3 4 5\sg(x)= 1/8 1/4 1/2 1 2
f(x) = 2x: (1, 2), (2, 4), (3, 6), (4, 8), (5, 10) (5, 10)
g(x) = f(1/x) = 2x: (1, 2), (1/2, 1), (1/3, 2/3), (1/4, 1/2), (1/5, 2/5)
The appropriate choices are thus:
A reflection of the graph of f(x) about the line y = x is the graph of g(x).
The two graphs are oriented and have the same form in common.
The moment where the two graphs come together (1, 2).
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solve and SHOW working
4^x = 8^ x - 1
The solution of the exponential equation is x = 0.35
What is an exponential equation?An exponential equation is an equation that contains exponents.
Since we have the exponential equation
4ˣ = 8ˣ - 1
We proceed to solve as follows
4ˣ = 8ˣ - 1
(2²)ˣ = (2⁴)ˣ - 1
(2ˣ)² = (2ˣ)⁴ - 1
Let 2ˣ = y
So, we have that
y² = y⁴ - 1
Re- arranging, we have that
y⁴ - y² - 1 = 0
Also, let y² = p. So, we have that
p² - p - 1 = 0
Now, we find p using the quadratic formula.
[tex]p = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex]
where a = 1 b = -1 and c = -1
So, [tex]p = \frac{-(-1) +/-\sqrt{(-1)^{2} - 4(1)(-1)} }{2(1)}\\= \frac{1 +/-\sqrt{1 + 4} }{2}\\= \frac{1 +/-\sqrt{5} }{2}\\p = \frac{1 + 2.24 }{2} or p = \frac{1 - 2.24 }{2}\\p = \frac{3.24 }{2} or p = \frac{-1.24 }{2}\\p = 1.62 or p = -0.62[/tex]
We ignore the negative value.
So, p = 1.62
y² = 1.62
y = ±√1.62
y = ±1.273
Since y = 2ˣ, we have that
2ˣ = ±1.273
We ignore the negative value since the value of y cannot be negative.
So, 2ˣ = 1.273
Taking natural logarithm of both sides, we have that
㏑2ˣ = ㏑1.273
x㏑2 = ㏑1.273
x = ㏑1.273/㏑2
= 0.2412/0.693
= 0.348
≅ 0.35
So, x = 0.35
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