Answer:
Answer c 1,800
Step-by-step explanation:
The total interest at the rate of 4.5% interest of the amount of $8000 will be $1800 hence option (C) will be correct.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.
Simple interest has a constant principal amount, as opposed to compound interest, which multiplies the interest from the principal of previous years to calculate the interest of the subsequent year.
Given that
Principle amount (P) = $8000
Rate of interest (R) = 4.5%
Time period (T) = 5 years.
The interest in the T time period has been given by
Total interest = PRT/100
So,
Total interest = 8000×4.5×5/100 = 1800
So total interest of the given amount will be $1800.
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Animal House Rescue is holding a fundraiser raffle. They sell 2,980 tickets for $1 each for a prize telescope valued at $425. What is the expected gain or loss to a participant purchasing ten tickets?
Answer:
Gain: $415
Loss: $10
Step-by-step explanation:
money earned - money spent = gain/loss
The gain is when the participant wins the telescope:
telescope = $425 ==> money earned
10 tickets * $1 = $10 for tickets ==> money spent
$425 - $10 = $415
Loss is when the participant doesn't get the telescope:
$0 ==> money earned (No money earned)
10 tickets * $1 = $10 for tickets ==> money spent
$0 - $10 = -$10 gained
-$10 gained ==> $10 lost
Solution for 4x+3y=11 over 2x+y=7
Answer
x=-1/2,=29/4
explanation
In the figure below, N is between M and O, and O is between N and P. If NO=6, NP=8, and MP=16, find MO.
P
A line segment is merely a portion of a line, one with definite ends and a finite length.
What is a line?A line segment is merely a portion of a line, one with definite ends and a finite length. An object with only one dimension, a line has length but no width. A line is made up of several points that are endlessly stretched in the opposing directions. In a two-dimensional plane, it is specified by two points. Collinear points are described as two points that are on the same line.
An endlessly long, two-directional line is referred to as a line. It just has one, and that is length. Collinear points are those that are situated along the same path. Two points make up a line, which is written as follows with an arrowhead: AB.
O is between M and P, and N is the midpoint of MO. IF NO=3 and MP = 10, find OP.
Given the following details as:
N is between M and O.
O is between N and P .
NO=6 and NP = 8.
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HELP !!!
write days in May and days in a year as a ratio
The ratio of days in May and days in a year is 31 to 365 or 31:365
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We need to find the days in May and days in a year as a ratio
Therefore, Days in may = 31
Days in a year = 365
Thus, the expected ratio = 31/365
Or
31:365
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a) What type of triangle is triangle ABC? b) Give reasons for your answer. I need the correct answer for B with Reasons Not "ab and ac are the same" any word other than the same
Answer:
Isosceles triangle
Step-by-step explanation:
Thorough explanation: Through the angles in the triangle ABC.
First, observe that angle ACD = 50 degrees (given)
Since lines AB and DE are parallel to each other,
angle BAC = angle ACD = 50 degrees (by the property of alternate angles)
It is also given that angle ABC = 80 degrees.
Since ABC is a triangle, the sum of the three angles must add up to 180 degrees.
Angle BAC + Angle ABC + Angle ACB = 180 degrees
50 + 80 + Angle ACB = 180
Angle ACB = 180 - 50 - 80
= 50 degrees
Since two of the angles, angles ACB and BAC are the same at 50 degrees, triangle ABC is an isosceles triangle. (With sides AB and BC equal)
How do you calculate seed multiplication ratio?
The number of seeds produced from a single seed when it is sown and harvested is referred to as the seed multiplication ratio.
What is Seed?A seed is an undeveloped plant embryo and food reserve that is encased in a protective outer covering in botany. More broadly, "seed" refers to anything that can be sown, which could include seed and husk or tuber.
Seeds are the result of a ripened ovule being fertilised by sperm from pollen, resulting in a zygote. The embryo within a seed develops from the zygote, forming a seed coat around the ovule and growing to a certain size within the mother plant before growth stops.
The formation of the seed is a step in the reproduction process of seed plants (spermatophytes). Other plants, such as ferns, mosses, and liverworts, do not have seeds and must reproduce through water-based means.
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. A polling organization announces that the proportion of American voters who favor congressional term limits is 64%, with a 95% confidence margin of error of 3%. If the opinion poll had announced the margin of error for 80% confidence rather than 95% confidence, this margin of error would be (a) 3%, because the same sample is used. (b) less than 3%, because we require less confidence. (c) less than 3%, because the sample size is smaller. (d) greater than 3%, because we require less confidence. (e) greater than 3%, because the sample size is smaller.
When C.I. is given as 80% then the margin of error will be 1.9591% as calculated from the given data.
We are given that the first margin of error (MOE) is 3%.
Also, confidence interval
first C.I.=95%
second C.I.=80%
Therefore , MOE at 80% will be ,
The formula for proportion is given as (P),
P=x/n , here 64%.
The values are same or constant as in general, this means standard deviation is also constant
Now formula for MOE is given by
MOE = Z x ( SD ) / √n
where , Z is value for confidence interval
MOE ∞ Z-value
So we can say that ,
MOE = k x Z ( where k = proportionality constant).
So , for 95 % Z=1.96 and for 80% Z=1.28
MOE then calculated will be , 1.95% .
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A wedding menu has 5 starters, 3 mains, and 4 desserts. The list gives the meal options each attendee must choose from. a starter and a main, a main and a dessert, a starter, a main, and a dessert. How many different ways of choosing a meal for this wedding are there
There are 60 different ways of choosing a meal for this wedding.
How many different ways of choosing a meal?There were five distinct main courses available for selection.
There are a total of 15 possible main dish and salad combinations when ordering these 5 distinct main meals together with any one of the 3 available salads.
A total of 60 distinct main dishes, salads, and dessert combinations are conceivable by ordering one of the four potential deserts for each of the 15 various main meals and salad combinations.
60 distinct main dishes might be purchased since.
There are 60 different ways of choosing a meal for this wedding
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Julius is allowed to surf the internet for only 3 hours a week. He has already been online for 1 2/3 hours this week. Write and solve an inequality to find how much more time Julius can spend online this week.
The number of hours that Julius can spend online this week is 1 1/3 hours.
How to illustrate the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
Since Julius is allowed to surf the internet for only 3 hours a week. He has already been online for 1 2/3 hours this week.
This will be Illustrated as x.
x + 1 2/3 ≤ 3.
x ≤ 3 - 1 2/3
x ≤ 1 1/3.
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in a right triangle, the two sides adjacent to the right angle are known as the
Answer:legs
Step-by-step explanation: I cannot give a explanation since it is simply math, anything adjacent to a right angle is called a leg.
Answer: the legs? or opposite and hypotenuse.
Step-by-step explanation:
The 44 members of the glee club are trying to raise at least $6,000 so they can compete in the state championship. They already have $1,220. What inequality can you enter to find the amount each member must raise, on average, to meet the goal?
The inequality that represents the situation is
The inequality that represents the situation is 45x + 1240 ≥ 6000
There are 45 members overall.
If one individual contributes $x, then
The sum that 45 individuals together raised is then equal to 45x.
$6000 is the bare minimum necessary to enter the competition.
$1240 is the amount they already have.
Therefore, the amount they need to raise is $6000 minus $1240.
Inequality can be displayed as:
45x ≥ 6000 - 1240
This demonstrates that the total amount raised by 45 individuals (45x) should be equal to or more than the sum they need to raise ($6,000 - $1240).
change the equation's order;
45x + 1240 ≥ 6000
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What is the answer to g=6x for x
Answer:
The answer is x=g/6
Step-by-step explanation:
When solving an equation like this, you want to move x over to the left of =, which leaves g, and 6. now always remeber that the next variable, g for instance, will be the one divided by the factor, 6
The stem-and-leaf plot shows the ages of customers who were interviewed in a survey by a store. How many customers were older than 45
Customers older than 45 years are 11 in number. This can be solved using stem-and-leaf plot.
What is stem-and-leaf plot?A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. Data are organized as they are gathered using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. As each integer throughout the database is divided into a stem and a leaf, thus the name fits.
The last digit of each data point serves as the "leaf" in a stem and leaf plot, which divides the data into numerical points (the leading digit or digits).
The stem and leaf plot represents the age of store patrons. The leaf represents the unit digit, while the stem stands for the tens digit. 45 is not taken into account because the question asks us to determine the percentage of consumers who are over 45.
Customers older than 45 years old include: 48, 50, 50, 51, 55, 56, 62, 64, 65, 65, 73.
So, there are a total of 11 clients.
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The complete question is as follows:
The stem-and-leaf plot shows the ages of customers who were interviewed in a survey by a store. How many customers were older than 45
What is the range of the function y = startroot x 5 endroot? y greater-than-or-equal-to negative 5 y greater-than-or-equal-to 0 y greater-than-or-equal-to startroot 5 endroot
The range of the function y = √(x +5) is y ≥ 0
What is the range of the function?The domain of a function is the set of all possible values of x
The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.
we have
y = √(x +5)
Remember that the radicand of the function must be greater than or equal to zero
so (x +5) ≥ 0
solve for x
x ≥ -5
The domain is the interval ----> [-5,∞)
For x= -5
y = √(-5 +5) = 0
so
The range is the interval ----> [0,∞)
y ≥ 0
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You have 3 3/4 cups of nuts to divide evenly among 5 people. How many cups of nuts will each person get
Each will get 3/5 cups of nuts by ratio and proportion concepts.
What does ratio explain mean?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
We have to divide total nuts within 5 people.
so,
3 3/5 : 5
but first convert,
3 3/5 = 15/4
substitute,
15/4 : 5 = 15/20cups of nuts
simplify,
3/5 cups
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a. Kiran tried to double this recipe. He used 2 cups of
yogurt, 6 tablespoons of peanut butter, 5 teaspoons of
chocolate syrup, and 4 cups of crushed ice. He didn't
think it tasted right. Describe how the flavor of Kiran's
recipe compares to Clare's recipe.
Therefore , the solution to this problem of unitary method comes out to be he should use 4 teaspoons of chocolate syrup instead of 5.
Define unitary method.A single or distinct variable is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.
Here,
Given :This recipe was doubled by Kiran. He used 4 cups of crushed ice, 6 tablespoons of chocolate syrup, 6 tablespoons of peanut butter, and 2 cups of yogurt.
1. Kiran's smoothie would be more chocolatey than Clare's. All ingredients are doubled, but there is an extra teaspoon of chocolate syrup in his smoothie.
2. Answers vary. Sample response: he should use 4 teaspoons of chocolate syrup instead of 5.
Therefore , the solution to this problem of unitary method comes out to be he should use 4 teaspoons of chocolate syrup instead of 5.
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PLEASE HELPPP
Given the diagram below, which statement is true?
∠1 and ∠3 are vertical angles and congruent.
What is congruence?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
What are vertical angles?
The opposing angles form when two lines cross. They are constantly on par. In this illustration, the angles a° and b° are vertical. The term "vertical" refers to the vertex, not up or down, where they cross.
Here,
we have given a diagram and we have to determine which statement is true that satisfies the true conditions.
By applying congruent property. we get
∠1 = ∠3 are vertivally opposite angle.
This is the only condition that satisfy the true condition from given statement.
Hence, ∠1 and ∠3 are vertical angles and congruent.
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Solve x=[tex]\sqrt{x} b^2-4ac\frac{x}{y} 2a[/tex]
The solutions to the quadratic function y = x² + 4x + 3, using the quadratic formula, are given as follows:
x = -1 and x = -3.
How to solve a quadratic function?The standard definition of a quadratic function is given as follows:
y = ax² + bx + c.
In which the leading coefficient a must assume a value different of zero.
The solutions to the quadratic function ax² + bx + c = 0 are obtained using the quadratic formula, as follows:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
The quadratic function for this problem is defined as follows:
x² + 4x + 3 = 0.
Hence the coefficients are:
a = 1, b = 4, c = 3.
The first solution is:
[tex]x = \frac{-4 - \sqrt{4^2 - 4(1)(3)}}{2} = -3[/tex]
The second solution is:
[tex]x = \frac{-4 + \sqrt{4^2 - 4(1)(3)}}{2} = -1[/tex]
Missing InformationThis problem was incomplete, hence the quadratic formula is used to solve y = x² + 4x + 3, as an example.
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Find the perimeter of a rectangle with the width (w) that is 12 cm less than the length (L).
Answer:
4x-24
Step-by-step explanation:
assume x=Length
perimeter
= x+(x-12)+x+(x-12)
= x+x -12+x+x-12
=4x-24
Which of the following lists of ordered pairs is a function?
Answer:
C is a function
Step-by-step explanation:
for a relation to be a function each value of x must map to exactly one unique value of y
A
2 → 5 and 2 → 2 ← not a function
B
- 1 → 6 and - 1 → 7 ← not a function
C
all values of x map to exactly one unique y ← function
D
3 → 1 and 3 → 2 ← not a function
sqrt{2x-1}-x=-8
solve for x
The values of x are 5 or 13.
What are equations?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given is an equation, [tex]\sqrt{2x-1}[/tex] - x = -8
[tex]\sqrt{2x-1}[/tex] - x = -8
[tex]\sqrt{2x-1}[/tex] = -8+x
Squaring both sides,
2x-1 = x²+64-16x
x²-16x-2x+1+64 = 0
x²-18x+65 = 0
Factorizing the equation,
x²-18x+65 = 0
x²-13x-5x+65 = 0
x(x-13)-5(x-13) = 0
(x-5)(x-13) = 0
x = 5 or 13
Hence, the values of x are 5 or 13.
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He starts by running 3 miles during every training session. Each week he plans to increase the distance of his run by 1/4 mile
The arithmetic expression may be used to get the formula T = (11 + w)/4, which is the distance Kane runs in a training session after w weeks.
Every training session, Kane begins out by running 3 miles, and he has a plan to improve that distance by 1/4 mile each week.
The number of weeks is w.
The arithmetic progression may be used to calculate an expression that displays the distance Kane runs during a training session after w weeks.
T = A + (n-1)d is the formula for the nth term in an arithmetic operation, where an is the first term, which is 3, d is the difference between two consecutive terms, which is, is the last term, and n is the total number of terms.
We get, T = (11+w)/4
This is the expression to show the distance Kane runs in a training session after w weeks.
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Complete question - Kane is training for a marathon. He starts by running 3 miles during every training session each week plans to increase the distance of his runs by 1/4 mile. Let w be the number of weeks. Write and expression to show the distance Kane runs in a training session after w weeks
73. Angle of elevation: In 2001, the tallest building in the world was the Petronas Tower
in Kuala Lumpur, Malaysia. For a person standing 25.9 ft from the base of the tower.
the angle of elevation to the top of the tower is 89°. How tall is the Petronas tower?
Analo
The Petronas tower is 1483.811 feet tall.
What is tangent function?One of the six fundamental functions in trigonometry is the tangent function. As stated, Tan A = Opposite Side/Adjacent Side is the Tangent Formula. Tangent may be modeled using sine and cosine as follows: Tan A = Sin A / Cos A.
Given:
Angle of elevation: In 2001, the tallest building in the world was the Petronas Tower in Kuala Lumpur, Malaysia.
For a person standing 25.9 ft from the base of the tower.
The angle of elevation to the top of the tower is 89°.
Let c = height of the tower,
and a = distance from the base of the tower to x.
a = 25.9 feet.
The formula:
Tangent (angle) = opposite side / adjacent side.
tan89° = c / a
57.29 = c / 25.9
c = 57.29 x 25.9
c = 1483.811 feet
Therefore, 1483.811 feet is the height of the Petronas tower.
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At Central Middle School the 108 students who take the AMC 8 meet in the evening to talk about problems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of 15 cookies, lists these items: 1/2 cups of flour 2 eggs, 3 tablespoons butter, 3/4 cups sugar 1 package of chocolate drops They will make only full recipes, no partial recipes. They learn that a big concert is scheduled for the same night and attendance will be down 25%. How many recipes of cookies should they make for their smaller party? (Some eggs and some cookies may be left over. )
(A) 1.
(B) 2.
(C) 5.
(D) 7.
(E) 15
The correct option is option (E) 15
To calculate the number of cookies they will need, they first determine the number of students who will be attending the meeting. Since attendance is down by 25%, the number of students attending is 108*(1-0.25) students.
=108 students * 0.75 = 81 students.
To figure out the number of cookies they will need, they multiply the number of students by the number of cookies per student, which is 81 students * 2 cookies= 162 cookies.
Since each recipe makes 15 cookies, they need to make 162 cookies / 15 cookies/recipe = 10.8 recipes.
Since they cannot make partial recipes, they round up and make 11 recipes of cookies for their smaller party.
As 11 is not a given option, we consider the option which is greater than 11, which is 15.
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Interest earned- $25
principal- $500
interest rate -???
time- 2 years
what is the interest rate
The interest rate is 2.5 %.
Simple interest is the form of interest used for short term loans, such as one receives at pawnshops or from loan sharks. It is governed by the formula:
I = Prt
where I is the amount of interest, P is the principal (amount of money borrowed), r is the interest rate (per year), and t is the time (expressed in years).
Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
I = $25, P = $500, r = ?, t = 2 years
∴ I = Prt
∴ r = I / Pt
∴ r = 25 / ( 500 * 2)
∴ r = 25 / 1000
∴ r = 0.025
∴ r = 0.025 * 100 %
∴ r = 2.5 %
Therefore, the interest rate is 2.5 %.
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Approximately 297 million guests visit the 400 American amusement parks annually, and take 1.7 billion safe rides. The National Safety Council publishes a report titled "Fixed-Site Amusement Ride Injury Survey" for the International Association of Amusement Parks and Attractions. The number of injuries per million patron-rides, X, has a Poisson distribution with parameter 0.8. In one million patron-rides, what is the probability that there are
a) No injuries?
b). More than TWO injuries?
The probabilities are given as follows:
a) No injuries: 0.4493 = 44.93%.
b) More than two injuries: 0.0474 = 4.74%.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following equation:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.The mean for this problem is of:
[tex]\mu = 0.8[/tex]
The probability of no injuries is of P(X = 0), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]
The probability of more than two injuries is of:
P(X > 2) = 1 - P(X <= 2)
In which:
P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)
Hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]
[tex]P(X = 1) = \frac{e^{-0.8}(0.8)^{1}}{(1)!} = 0.3595[/tex]
[tex]P(X = 2) = \frac{e^{-0.8}(0.8)^{2}}{(2)!} = 0.1438[/tex]
Then:
P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.4493 + 0.3595 + 0.1438 = 0.9526.P(X > 2) = 1 - P(X <= 2) = 1 - 0.9526 = 0.0474.More can be learned about the Poisson distribution at https://brainly.com/question/7879375
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Vanessa will sell yogurt for $2.50 a cup. Fill in the table to show how much money Vanessa will make if she sells 19 cups of vanilla yogurt.
Answer:
2.50 × 19 = 47.5
Therefore, she would get $47.5 if she sold 19 cups.
Ava bought 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. Grace spent $254 buying 14 packages of tulip bulbs and 12 bags of daffodil bulbs. Use elimination to solve the system of linear equations and determine how much one package of tulips bulbs costs, x, and how much one bag of daffodil bulbs costs, y. Enter your answer as an ordered pair (x,y).
When Ava purchased six packages of tulip bulbs and twelve bags of daffodil bulbs, the price per tulip bulb was $7 and the price each daffodil bulb was $13.
what is linear equations ?The algebraic equation y=mx+b is known as a linear equation. M serves as the y-intercept, and B serves as the slope. The previous clause has two variables, y and x, and is sometimes referred to as a "linear equation with two variables". Bivariate linear equations are those with two independent variables. The following are a few examples of system of equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation takes the form y=mx+b, with m denoting the slope and b denoting the y-intercept, it is referred to as being linear. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
Let x be the price of a single tulip bag.
Y should equal the price of one bag of daffodil bulbs.
Grace = 14x + 12y = 254
ava = 6x + 12y = 198
- 8x = - 56
x = - 56/-8
x = 7.
Equation 1 becomes
6* 7 + 12y = 198
42 + 12y = 198 when x = 7 is substituted.
12y = 198 - 42
12y = 156
y = 156/12
y = 13
When Ava purchased six packages of tulip bulbs and twelve bags of daffodil bulbs, the price per tulip bulb was $7 and the price each daffodil bulb was $13.
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Tran is making fasnachts (deep-fried German doughnuts) to sell the
Tuesday before Ash Wednesday, her bakery's biggest fasnacht day of
the calendar year. She has 8 pounds of butter and her recipe calls for
1/4 cup of butter per 2 dozen
fasnachts. If 1 pound of butter is 2 cups,
then how many individual fasnacht doughnuts will Tran be able to
make?
Answer:
1,536
Step-by-step explanation:
1 pound equals 2 cups, so 8 pounds will be 16 cups.
[tex]\frac{16}{\frac{1}{4} }[/tex] = 16 x 4 = 64
She can make 64 2 dozen fasnachts. There are 24 fasnachts in 2 dozen.
64 x 24 = 1536 individual fasnachts doughnuts.
What’s the slope of the line going though the points (12,0) and (12,9)
Answer:
infinity/undefined (both are acceptable)
Undefined is actually the best answer in college but your answer key might put it as infinity.
Step-by-step explanation:
Observe that the x coordinates of the two points are exactly the same at 12.
This reduces the possibility of the line being a horizontal or a vertical line.
Imagine, if x coordinates is always the same, it means that you are only varying y and that happens when you move up and down the graph.
Hence, the line is a straight vertical line. (Line equation: x = 12)
Gradient/Slope of a vertical line = infinity/undefined.
The slope of the given line is Undefined
The slope of the line when two points in the line is given is given by
m=(y₂-y₁)/(x₂-x₁)
The points are (12,0) and (12,9)
m=(9-0)/(12-12)
= 9/0
=Undefined
The slope of the line is Undefined
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https://brainly.com/question/29205562?referrer=searchResults