Answer:
Alan had 272 cards initially and Ben had 88 cards initially.
Step-by-step explanation:
Let's start by assuming that Alan had x cards and Ben had y cards initially. We know that the sum of their cards is 360, so:
x + y = 360
In the first game, Alan lost 2/5 of his cards to Ben, so he gave away (2/5)x cards to Ben. Therefore, he was left with:
(3/5)x cards
Ben received (2/5)x cards from Alan and had y cards initially, so he had:
y + (2/5)x
cards after the first game.
In the second game, Alan won 1/4 of Ben's cards, so he received (1/4)(y + (2/5)x) cards. Therefore, he had:
(3/5)x + (1/4)(y + (2/5)x)
cards after the second game.
In the third game, Alan lost 1/6 of his cards to Ben, so he gave away (1/6)(3/5)x cards to Ben. Therefore, he was left with:
(2/3)(3/5)x = (2/5)x
cards.
Ben received (1/6)(3/5)x cards from Alan in the third game, and he had y + (2/5)x cards after the first game. Therefore, he had:
y + (2/5)x + (1/6)(3/5)x = y + (9/25)x
cards after the third game.
Since both boys ended up with the same number of cards, we can set the expressions for their final card counts equal to each other:
(3/5)x + (1/4)(y + (2/5)x) = y + (9/25)x
Multiplying both sides by 100 to get rid of the fractions, we get:
60x + 25y + 50x = 100y + 36x
Simplifying, we get:
24x = 75y
Since x + y = 360, we can use this equation to solve for one of the variables in terms of the other:
x = 360 - y
Substituting into the equation we just obtained, we get:
24(360 - y) = 75y
Simplifying, we get:
8640 - 24y = 75y
99y = 8640
y = 87.27
Since y must be a whole number (since it represents the number of cards that Ben had initially), we can round it up to 88. Substituting into the equation x + y = 360, we get:
x + 88 = 360
x = 272
Therefore, Alan had 272 cards initially and Ben had 88 cards initially.
To find the initial number of game cards Alan and Ben had, we can set up an equation and solve for a variable. The equation involves using the information about the games played and the number of cards lost and gained by Alan. The solution will give us the initial numbers of cards for both boys.
Explanation:To solve this problem, let's assume that Alan had x cards and Ben had y cards at the beginning. We are given that Alan lost 2/5 of his cards to Ben in the first game, so he had (3/5)x cards left and Ben had y + (2/5)x cards. In the second game, Alan won 1/4 of Ben's cards, so he gained (1/4)(y + (2/5)x) cards, leaving him with (3/5)x + (1/4)(y + (2/5)x) cards. In the last game, Alan lost 1/6 of his cards to Ben, so he had (5/6)((3/5)x + (1/4)(y + (2/5)x)) cards left. Since both boys had the same number of cards in the end, we can set up the equation: (5/6)((3/5)x + (1/4)(y + (2/5)x)) = y + (2/5)x. After simplifying and solving for y in terms of x, we can substitute back into the equation to find the value of x.
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The following histogram shows the number of items sold at a grocery store at various prices: Histogram titled Items Sold with Price Range on the x axis and Number of Items Sold on the y axis. Bar 1 is 0 to 2 dollars and 50 cents and has a height of 2. Bar 2 is 2 dollars and 51 cents to 5 dollars and has a height of 4. Bar 3 is 5 dollars and 1 cent to 7 dollars and 50 cents and has a height of 0. Bar 4 is 7 dollars and 51 cents to 10 dollars and has a height of 1. Which of the following data sets is represented in the histogram? {0.50, 2.00, 2.52, 3.37, 4.53, 5.00, 8.99} {2, 4, 0, 1} {2.50, 2.51, 5.00, 5.01, 7.50, 9.00, 10.00} {0.50, 2.50, 2.50, 5.00, 5.00, 5.00, 7.51}
The second bar represents the price range from $2.51 to $5.00, so the data set includes the value of 4.53 and the value of 5.00 the correct answer is {0.50, 2.00, 2.52, 3.37, 4.53, 5.00, 8.99}
What is the histogram?A histogram is a graph used to represent the frequency distribution of a few data points of one variable. Histograms often classify data into various “bins” or “range groups” and count how many data points belong to each of those bins.
The histogram shows the number of items sold at various price ranges, and the heights of the bars indicate the number of items sold within each price range.
The data set that is represented in the histogram is:
{0.50, 2.00, 2.52, 3.37, 4.53, 5.00, 8.99}
This is because the histogram has four bars with heights of 2, 4, 0, and 1, which correspond to the number of items sold in each of the four price ranges shown.
The values in the data set correspond to the boundaries of these price ranges. For example, the first bar represents the price range from $0.00 to $2.50, so the data set includes the value 2.00 (which is within this range) and the value 2.52 (which is just outside this range).
Similarly, the second bar represents the price range from $2.51 to $5.00, so the data set includes the value of 4.53 (which is within this range) and the value of 5.00 (which is the upper boundary of this range).
Therefore, the second bar represents the price range from $2.51 to $5.00, so the data set includes the value of 4.53 and the value of 5.00 the correct answer is {0.50, 2.00, 2.52, 3.37, 4.53, 5.00, 8.99}
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A field is in the shape of a square. The length of the field is 5x³y5. What is
the area of the field terms of x and y?
Answer: The area of a square is given by the formula A = s^2, where s is the length of a side of the square.
In this case, the length of the field is 5x³y5, so each side of the square is also 5x³y5. Therefore, the area of the square can be found as:
A = (5x³y5)^2
A = 25x^6y^10
So the area of the field in terms of x and y is 25x^6y^10.
Step-by-step explanation:
Super Scary Circles Test #10
This figure is NOT drawn to scale.
a = 90°
b = 12°
C =
d =
e=
f=
g=
h=
i =
j=
Can anyone pls help me with this . We are solving for the angles and I need this done tmr .
The measures of the angles obtained using circle theorems are presented as follows;
a = 90°, b = 12°, c = 64°, d = 54°, e = 54°, f = 48°, g = 66°, h = 32°, i = 36°, and j = 20°
What are circle theorems?Circle theorems are theorems that indicates the relationships between angles, sector, chords, and tangent in a circle.
Please find the possible drawing in the question created with MS Word
a + a = 2·a = 180° (Linear pair angles)
a = 180°/2 = 90°
a = 90°
The right triangle with the acute angle angle of 78° indicates;
b = 90° - 78° = 12°
b = 12°
The angle at the center theorem indicates that we get;
The base angle of the large isosceles triangle = 2 × 32° = 64°
∠c is a base angle of the large triangle, therefore;
c = 64°
2·c + d = 180°
d = 180° - 2 × 48° = 54°
e = d = 54°
e = 54°
The angle at the circumference of the circle with angle ∠g and and ∠f = 4·b
Angle at the circumference = 4 × 12° = 48° = ∠f
f = 48°
Angle ∠g is equivalent to a base angle of the isosceles triangle, therefore;
∠g = (180° - 48°)/2 = 66°
g = 66°
Angle at the vertex of the triangle with angle h is equivalent to the base angle of the large triangle, therefore;
2·h = 64°
h = 64°/2 = 32°
h = 32°
Angle at the center = 2 × (180° - 2 × 48°) = 168°
5b + 2f + i + 168° = 360° (Angle sum property of a quadrilateral)
i = 360° - (5b + 2f + i + 168)
i = (360 - (5×12 + 2×48 + 168) = 36
i = 36
5b + 2h + i + j = 180
j = 180 - (5b + 2h + i)
j = 180 - (5 × 12 + 2 × 32 + 36) = 20°
j = 20°
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What is $54.28 rounded to the nearest 10 dollars?
$54.28 rounded to the nearest 10 dollars is $50.00
how do you know that 8:12 is equivalent to 4:6
Answer: it is 4:2
Step-by-step explanation: because it is a ratio, both sides can be divided by the same number and still have the same meaning. btw in this case both divided by 2
A spice box manufacturing company is having difficulty filling packets to the required 50 grams. Suppose a business researcher randomly selects 60 boxes, weighs each of them and computes its mean. By chance, the researcher selects packets that have been filled adequately and that is how he gets the mean weight of 50 g, which falls in the "fail to reject" region.
The decision is to fail to reject the null hypothesis even though population mean is NOT actually 50 g.
Which kind of error has the researcher done in this case?
Answer: The researcher has made a Type II error in this case.
A Type II error occurs when the null hypothesis is not rejected even though it is false, i.e., the researcher fails to detect a significant difference when one actually exists. In this case, the null hypothesis is that the mean weight of the spice packets is 50 g, and the researcher has failed to reject this null hypothesis based on the sample mean of 50 g.
However, the population mean is not actually 50 g, and the researcher has made an error in failing to detect this difference. The sample size of 60 boxes may not have been large enough to detect a significant difference, or there may have been other factors that affected the measurements.
Therefore, the researcher has made a Type II error in this case by failing to reject the null hypothesis when it is actually false.
Step-by-step explanation:
The equation y = 19(1.057) represents book sales in billions of dollars since 1990. Let x represent the number of years. Let x = 0 represent book sales in 1990. What were the total sales, in billions of dollars, in 1990? O 18 19 O 20 O 21 B 7 8. 9 10 Next
In 1990, 19 billion dollars worth of books were sold.
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]
The formula for exponential decay is [tex]y = y_0e^{(-kt)}.[/tex]
We know a function is called an exponential function when the independent variable is the exponent.
An example of an exponential function is, aˣ.
Given, The equation y = 19(1.057) represents book sales in billions of dollars since 1990.
The equation is, y = 19(1.057)ˣ, Where x = the number of years.
Therefore, At x = 0 or in 1990,
y = 19(1.057)⁰.
y = 19(1).
y = 19 billion dollars
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w is less than 7 and greater than or equal to -5 write the following as an inequality
Someone help me with these 3 math problems.
1. The value of the variable 'x' is 10 that is written as x = 10.
2. The equation is ∠3 + ∠4 = 90°. Then angles ∠3 and ∠4 will be complementary angles.
3. The measure of angle ∠2 is 60° which is an acute angle.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
1. ∠1 = 6x + 45 and ∠3 = 9x + 15
Angle ∠1 and angle ∠3 are opposite angles. Then the equation is given as,
∠1 = ∠3
9x + 15 = 6x + 45
9x - 6x = 45 - 15
3x = 30
x = 30 / 3
x = 10
2. Angle ∠2, angle ∠3, and angle ∠4 are supplementary angles. Then the equation is given as,
∠2 + ∠3 + ∠4 = 180°
90° + ∠3 + ∠4 = 180°
∠3 + ∠4 = 90°
3. Angle ∠1 is 120°, then the measure of angle ∠2 is given as,
∠1 + ∠2 = 180°
120° + ∠2 = 180°
∠2 = 60° (acute)
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The quadrants go in counter-clockwise position.
O True
O False
Answer:true
Step-by-step explanation:
can someone tell me the answers to b. and c.
1. The Range of Elevation for Long beach is 367 feet.
2. The Range of Elevation for New Orleans is 33 feet.
3. New Orleans have the average of 2 feet below sea.
What is Range?In statistics, the range is the difference between the highest and lowest values for a given data collection.
Given:
1. The Range of Elevation for Long beach
= Highest - Lowest
= 360 - (-7)
= 360 + 7
= 367 feet
2. The Range of Elevation for New Orleans
= Highest - Lowest
= 25- (-8)
= 25+ 8
= 33 feet
3. New Orleans have the average of 2 feet below sea.
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1. Rectangle EFGH with vertices E(1,-1), F(4, -1), G(4,-5),
and H(1, -5); scale factor: k = 3,
center of dilation: (2, -4)
Answer:
The new vertices of the rectangle after applying a scale factor of 3 with a center of dilation at (2, -4) are E'(-1, -11), F'(7, -11), G'(7, -15), and H'(-1, -15
Step-by-step explanation:
In a population of mendel's garden peas, the frequency of dominant yellow-flowered plants is 50%. The population is in hardy-weinberg equilibrium. What is the frequency of the recessive allele in the population?.
Answer:
the frequency of the recessive allele in the population is 0.5 or 50%.
Step-by-step explanation:
In a population in Hardy-Weinberg equilibrium, the frequency of alleles remains constant from generation to generation. According to the Hardy-Weinberg law, if p is the frequency of the dominant allele and q is the frequency of the recessive allele, then:
p + q = 1
and
p^2 + 2pq + q^2 = 1
where p^2 represents the frequency of homozygous dominant individuals, 2pq represents the frequency of heterozygous individuals, and q^2 represents the frequency of homozygous recessive individuals.
Given that the frequency of dominant yellow-flowered plants is 50%, or 0.5, we can assume that p = 0.5. Substituting into the first equation, we get:
0.5 + q = 1
Solving for q, we get:
q = 1 - 0.5
q = 0.5
Therefore, the frequency of the recessive allele in the population is 0.5 or 50%.
Elsa menabung uang di bank sebesar Rp.2.000.000,00. Apabila ia mendapat bunga 0,5% perbulan, berapa jumlah uang tabungan di bank selama 10 bulan?
Answer:
Jumlah uang tabungan Elsa setiap bulan dapat dihitung dengan rumus:
A = P(1 + r)^n
dimana:
A = jumlah uang tabungan akhir
P = jumlah uang tabungan awal
r = tingkat bunga per bulan (dalam desimal)
n = jumlah bulan
Dalam kasus ini, P = Rp.2.000.000,00, r = 0,5% atau 0,005 per bulan, dan n = 10 bulan.
Maka,
A = 2.000.000(1 + 0,005)^10
= 2.000.000(1,005)^10
= 2.000.000(1,0512)
= Rp.2.102.400,00
Jadi, jumlah uang tabungan Elsa di bank setelah 10 bulan adalah Rp.2.102.400,00.
Step-by-step explanation:
Match each equation on the left to the mathematical property it uses on the right.
(a) Commutative property of addition , (b) Distributive Property , (c) Associative Property of Multiplication , (d) Commutative property of multiplication and (e) Associative property of addition.
What is Associative Property ?
The associative property is a mathematical principle that states that the way in which factors are grouped in a multiplication or addition expression does not affect the final result. In other words, when using the associative property, we can add or multiply a group of numbers in any order we want, as long as we keep the order of the individual numbers the same.
(7 + 3) + 2 = 2 + (7 + 3) Commutative property of addition
3(2x +4) = 6x + 12 Distributive Property
(9 * x) * 3 = 9 * (x * 3) Associative Property of Multiplication
(8 * x * 2) = (8 * 2* x) Commutative property of multiplication
(4 + 5) + 1 = 4 + (5 + 1) Associative property of addition
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- The water level in a retention pond started at 5 ft (60 in.) and decreased at a rate of 2 in./day during a 14-day drought. A tropical depression moved through at the beginning of the 15th day and produced rain at an average rate of 2.5 in./day for 5 days. Write a piecewise-defined function to model the water level L (x) (in inches) as a function of the number of days x since the beginning of the drought.
The piecewise function that models model the water level L (x) (in inches) as a function of the number of days x since the beginning of the drought is given as follows:
L(x) = 60 - 2x, 0 ≤ x ≤ 14.L(x) = 30 + 5x, 15 ≤ x ≤ 19.How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which;
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.A piecewise function is a function with different definitions, based on the input of the function.
For the first 14 days, the parameters are given as follows:
b = 60 -> water level during day 0.m = -2 -> each day the amount decreased by 2 in.Hence:
L(x) = 60 - 2x, 0 ≤ x ≤ 14.
For the last 5 days, the parameters are obtained as follows:
b = 60 - 2(15) = 30.m = 5, as each day the amount increased by 2 in.Hence:
L(x) = 30 + 5x, 15 ≤ x ≤ 19.
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tommmy earns $140 in interest after 5 years on a pricipal of $400 jane earned $132 after 4 years on principal of $600 use the intrest rate to justify which bank would you rather use tommys or janes
Comparing the interest rates of Jane and Tommy, we can say that Tommy's bank is better because he earns more amount of money for less principal amount.
What is meant by the interest rate?The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.
The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.
Given,
Interest earned by Tommy SI = $140
Time t = 5 years
Principal amount P = $400
Interest earned by Jane SI = $132
Time t = 4 years
Principal amount P = $600
Simple interest SI = (P × r × t)/100
where r = interest rate
For Tommy,
140 = ( 400 × r × 5) /100
r = 7%
For Jane,
132 = ( 600 × r × 4) / 100
r = 5.5%
Therefore comparing the interest rates of Jane and Tommy, we can say that Tommy's bank is better because he earns more amount of money for the less principal amount.
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Can someone please help? Thank you
a. The six trigonometric functions of the angle β are:
sin β = 7/25
cos β = 24/25
tan β = 7/24
csc β = 25/7
sec β = 25/24
cot β = 24/7
b. Using trigonometric identity, cos X + (sin X)(tan X) = 1
What are the six trigonometric functionsWe can use the given value of cos β = 24/25 to find the other trigonometric functions of the angle β.
Let's draw a right triangle with angle β, adjacent side of length 24, and hypotenuse of length 25 (since cos β = adjacent/hypotenuse):
Using the Pythagorean theorem, we can find the opposite side:
Opposite side = sqrt(hypotenuse^2 - adjacent^2) = sqrt(25^2 - 24^2) = sqrt(49) = 7
So the triangle is:
Now we can find the other trigonometric functions:
sin β = opposite/hypotenuse = 7/25
cos β = adjacent/hypotenuse = 24/25
tan β = opposite/adjacent = 7/24
csc β = hypotenuse/opposite = 25/7
sec β = hypotenuse/adjacent = 25/24
cot β = adjacent/opposite = 24/7
2. We can use the trigonometric identity for tangent:
tan X = sin X / cos X
to rewrite the expression as:
cos X + (sin X)(sin X / cos X)
Multiplying through by cos X, we get:
(cos X)(cos X) + (sin X)(sin X)
Using the Pythagorean identity:
(sin X)^2 + (cos X)^2 = 1
we can simplify further:
1 - (cos X)^2 + (cos X)^2 = 1
So the final simplified expression is equal to 1
3. We can start with the left-hand side of the equation and manipulate it using the definitions of the trigonometric functions and the Pythagorean identity until we arrive at the right-hand side:
tan²α(csc²α - 1)
= (sin²α/cos²α)((1/sin²α) - 1)
= (sin²α/cos²α - sin²α/cos²α)
= 0
Now, let's look at the right-hand side:
1
We see that the left-hand side simplifies to 0, while the right-hand side is 1. Therefore, the identity is not true for all values of α.
We can see this more clearly by picking a specific value of α and evaluating both sides of the equation. For example, let's take α = 45°:
tan²45°(csc²45° - 1) = (1/1)((2/1) - 1) = 1
1 = 1
So the identity holds for α = 45°, but we have already shown that it does not hold for all values of α. Therefore, the identity is not true for all values of α.
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please help! Ill give the brainlist thing :)
The weight of the kitten is expected to rise by 0.2 ounces for every extra day after birth. The correct answer is B.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
For the first three months following birth, data on kitten weight (in ounces) was gathered. A line of fit was constructed through the scatter plot with the equation w = 2.75 + 0.2d, where w is the kitten's weight in ounces and d is the kitten's age in days.
For each additional day after the kitten is born, its weight is predicted to increase by 0.2 ounces. Then the correct option is B.
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I really need help with this
The prove that triangle ABE is congruent to triangle CDE is given below
What is congruence?Generally, To prove that triangle ABE is congruent to triangle CDE, we need to show that they have the same size and shape.
First, we can see that angle AED and angle CEB are opposite angles and therefore congruent, since AB || DC.
Also, since line AB = line DC, we know that segment AE is congruent to segment CE and segment BE is congruent to segment DE.
Using these congruent sides and the congruent angle, we can apply the Side-Angle-Side (SAS) congruence criterion to conclude that triangle ABE is congruent to triangle CDE.
Therefore, we have proven that triangle ABE is congruent to triangle CDE.
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1. Amy wants to her ice cream cone filled exactly to the top. The radius of the cone is 2 in. and the height is 6 in. How much ice cream will it take to fill the cone?
2. Jack is going to fill his beach ball with water. The radius of the ball is 24 in. How much water will it take to fill the beach ball?
3. Mary is sending her sister as summer camp a square box filled with tiny candies. The side of the box measures 6 in. How much candy will it take to fill the box?
4. Jim and Mary are competing in a math contest. They have to calculate how much it takes to completely fill a canister with a radius of 4 in. and a height of 5 in. with flour. How much flour will it take to fill the canister?
5. Aunt Lillian needs to fill a shoebox with packing material. The box measured 9 in by 5 in by 5 in. How much packing material does she need to fill the box?
(It doesn’t matter what the size, the formula stays the same….)\
PLEEAAASEEE HELLLP
1. The volume of a cone is 8π cubic inches.
2. The volume of a sphere is 8π cubic inches.
3. The volume of a cube is 8π cubic inches.
4. The volume of a cylinder is 8π cubic inches.
5. The volume of a rectangular prism is 8π cubic inches.
What is volume?The volume of a thing is the area that it occupies in three dimensions. Space is what a thing occupies, to put it simply.
1. The volume of a cone is given by V = (1/3)πr²h, where r is the radius and h is the height. Substituting the given values, we get V = (1/3)π(2²)(6) = (4/3)π(6) = 8π cubic inches.
2. The volume of a sphere is given by V = (4/3)πr³, where r is the radius. Substituting the given value, we get V = (4/3)π(24³) = 18432π cubic inches.
3. The volume of a cube is given by V = s³, where s is the side length. Substituting the given value, we get V = 6³ = 216 cubic inches.
4. The volume of a cylinder is given by V = πr²h, where r is the radius and h is the height. Substituting the given values, we get V = π(4²)(5) = 80π cubic inches.
5. The volume of a rectangular prism is given by V = lwh, where l, w, and h are the length, width, and height, respectively. Substituting the given values, we get V = (9)(5)(5) = 225 cubic inches.
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Write down the two inequality equations that go with this graph below:
Label your answer the RED or Pink inequality equation and
Label your answer the BLUE inequality equation.
There are 3 parts to each inequality equation, you can get points for each part correct (y axis intercept, slope, and the correct Inequality symbol).
The system of inequalities is y < x + 2 and 5y ≤ -2x + 10
How to determine the system of inequalityFrom the question, we have the following parameters that can be used in our computation:
The blue and the red lines
For the blue line, we have the following points
(0, 2) and (-2, 0)
The equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx + 2
Using the points, we have
-2m + 2 = 0
m = 1
So, we have
y = x + 2
The lower part is shaded and the line is a dotted line
So, we have
y < x + 2
For the red line, we have the following points
(0, 2) and (5, 0)
The equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx + 2
Using the points, we have
5m + 2 = 0
m = -2/5
So, we have
y = -2/5x + 2
The lower part is shaded and the line is a shaded line
So, we have
y ≤ -2/5x + 2
Multiply through by 5
5y ≤ -2x + 10
Hence, the system is y < x + 2 and 5y ≤ -2x + 10
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2 the length of a rectangular picture frame is 3 inches shorter than its width if the perimeter of the picture frame is 38 inches what is the length i and width w of the frame write and solve an equation to model the problem explain the meaning of the solution
Answer:
Step-by-step explanation:
The length of a rectangular picture frame is 3 inches longer than it's width. If the perimeter of the picture frame is 38 Inches, what is the length and width ?
Given :
Perimeter of rectangle is 38 Inches
lenght is 3 inches more than the breadth.
let, width be x, and length be x+3
So, Breadth is 8 inches and length is 8+3= 11 inches.
Let's verify ::
Thus Solved !!
I need immediate help!!!! Please help!
Answer:
3×1×1.
Step-by-step explanation:
The restaurant gives us an Italian bread, a whole wheat role and a wrap:
Counted together that's 3.
Then they let us choose one type of meat:
Counted that's only 1.
Finally, they let us choose one type of cheese:
Counted that's also 1.
Together that makes 3×1×1.
Mr. Nunez is tracking the progress of his plants' growth. Today the first plant is 5 cm high and the plant grows 2
cm per day. The second plant is 3 cm high and grows 3 cm per day.
A. Find the equations that represent the plants'
height after any given number of days.
B. Graph the system of equations
C. How tall is each plant after 15 days?
The equations that represent the plants' height after any given number of days are as follows;
y = 2x + 5
y = 3x + 3
The height of the first plant is 33 cm.
The height of the second plant is 48 cm.
How to write a system of equations to describe the situation?Based on the information provided above, the first plant is 5 cm high and the plant grows 2 cm per day. Therefore, the total height, y, can be represented by this equation:
y = 2x + 5
where:
x represents the number of days.
For the second plant, we have:
y = 3x + 3
After 15 days, the total height of each plant is given by;
First plant, y = 2x + 5 = 2(15) + 3 = 33 cm.
Second plant, y = 3x + 3 = 3(15) + 3 = 48 cm.
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A cube has a length of 12 cm , what is its surface area?
72 sq. cm
1500 cubic cm
1728 sq cm
864 sq. cm
Answer:
864 sq cm
Step-by-step explanation:
Surface area of cube = 6 × (l)square units. = 6 × 12cm × 12cm = 6 × 144cm = 864cmsquare.
Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars.
Estimated Sales Volume=45.15+0.54(Advertising Expenditures)
If the company has a target sales volume of $125,000
, how much should the sales manager allocate for advertising in the budget? Round your answer to the nearest dollar.
Answer:
We can use the given equation to solve for the advertising expenditures needed to achieve the target sales volume of $125,000:
125 = 45.15 + 0.54x
where x is the advertising expenditures in thousands of dollars.
Simplifying the equation:
0.54x = 125 - 45.15
0.54x = 79.85
x = 79.85 / 0.54
x ≈ 147.69
Therefore, the sales manager should allocate about $147,690 for advertising in the budget to achieve the target sales volume of $125,000.
Step-by-step explanation:
What is the inequality shown?
-6
-3 -2
-4
-5
-1
0
1
2
3 4
15
5
916
From the image given, inequality is -2≤x<8 from x≥-2, x<8. It serves as a concrete example of inequality.
What is inequality?Broadly speaking, a mathematical phrase that defines an order relationship between two integers equivalent algebraic expressions, showing whether one is bigger than, equal to, smaller than, or smaller than and equal to the other.
The sentence "5x - 4 > 2x + 3" seems like an equation because the mathematical sign for "equals" has indeed been replaced by an arrowhead. It serves as a concrete example of inequality. From the image given, inequality is -2≤x<8 from x≥-2, x<8.
Therefore, from the image given, inequality is -2≤x<8 from x≥-2, x<8.
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Cera and Bethany save money using savings accounts
opened on the same day. Both deposit $20 to start and an
additional $15 each week. The graph represents the total
amount, y, in each savings account after x weeks. Describe
the number of solutions modeled in the graph and what it
means for the situation. How can you change the situation
so that the graphs model a different number of solutions?
Explain your reasoning
This could result in one, two, or multiple points of intersection, depending on the specific values of the deposits and the rates of increase.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
we can assume that the graph of Cera's and Bethany's savings accounts will show the total amount of money in their accounts after a certain number of weeks.
Since both Cera and Bethany deposit the same amount of money and make the same additional deposits each week, their savings will increase at the same rate. Therefore, the graph will likely show two parallel lines that start at $20 and increase by $15 per week.
The number of solutions modeled by the graph will depend on whether the two lines ever intersect. If the lines do not intersect, then there is no solution to the system of equations that model the two savings accounts. In other words, there is no point at which the total amount of money in both accounts is the same.
On the other hand, if the lines do intersect, then there is at least one solution to the system of equations. In this case, the point of intersection represents the week at which the total amount of money in both accounts is the same.
To change the situation so that the graphs model a different number of solutions, we could change the initial deposit or the amount of money deposited each week for one or both of the savings accounts. For example, if Cera starts with a higher initial deposit than Bethany, or if Cera deposits more money each week, then their savings will increase at different rates and the lines on the graph will not be parallel.
Therefore, This could result in one, two, or multiple points of intersection, depending on the specific values of the deposits and the rates of increase.
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Pictures are the questions.
The answer to the probabilities are: (a) 0.8, (b) 0.2 (c) 0.3 (d) 0.7
What is probability?Probability is a branch of mathematics used to measure how likely something is to happen. It is calculated by taking into account the chance that a given event will occur, as well as taking into account an exhaustive set of equally likely outcomes
The percentage of married women is 80%
the number of women is 10
The probability that all of them dislike their mother in-laws is
P(x) = Number of required outcome/Number of possible outcomes
80/100 * 10 = 8 women
a) P(All of them dislike their mother in-law is 8/10 = 0.8
b) P(none of them dislike their mother-in-law is
P(x) = 1 0.8 = 0.2
c) P(At least eight of them dislike their mother-in-law)
P(x) = 8, 9, 10 = 3
Therefore, the probability is 3/10 = 0.3
d) P(no more than seven dislike their mother in-law
1,2,3,4,5,6,7 = 7
P(x) = 7/10 = .0.7
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