Gregory has 10 ways to choose 3 boxes of cereal.
What do you mean by purchase?
A corporation or organization uses the purchasing process to buy products or services in order to achieve its objectives. Although many organizations make an effort to establish standards for the purchasing process, procedures can differ significantly between organizations.
According to data in the given question,
We have :
The purchase of 3 boxes and the store has 5 different varieties of munchie brand cereal.
The order in which the boxes of cereal are chosen is not important as Gregory can randomly choose any 3 different varieties. So, this is a combination problem.
Use the combination formula:
\(_nC_r=\dfrac{n!}{r!(n-r)!}\)
Putting n=5 (5 different varieties) and r=3 (3 different varieties). So, the number of ways Gregory choose 3 boxes of cereal is:
\(_{5}C_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!2!}= \frac{5.4.3.2.1}{3.2.1.2.1} _{5}C_3=\dfrac{5\cdot 4}{2\cdot 1}=10\)
Therefore, the required answer is 10 ways.
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crying for help here..
Answer:
ST=32
Step-by-step explanation:
We know the two sides are equal, so first solve for p.
9p-4=4p+16
9p-4p=16+4
5p=20
p=4
Now subsitute p back in for ST
9(4)-4=32
Determine whether the improper integral diverges or converges. integral_19^infinity cos (pi x) dx converges diverges Evaluate the integral if it converges. (If the quantity diverges, enter DIVERGES.)
The sine function oscillates between -1 and 1, the limit does not exist as b approaches infinity. Therefore, the improper integral diverges. The answer is: DIVERGES
The given improper integral is ∫19^∞cos(πx)dx. To determine whether it converges or diverges, we can use the following theorem:
If f(x) is continuous, positive, and decreasing on [a, ∞), then the improper integral ∫a^∞ f(x)dx converges if and only if the corresponding improper sum ∑n=a to ∞ f(n) converges.
In this case, f(x) = cos(πx), which is not positive and decreasing on [19, ∞). Therefore, we cannot use this theorem to determine whether the integral converges or diverges.
Instead, we can use the following test for convergence:
If f(x) is continuous and periodic with period p, and ∫p f(x)dx = 0, then the improper integral ∫a^∞ f(x)dx converges if and only if ∫a^(a+p) f(x)dx = ∫0^p f(x)dx converges.
In this case, f(x) = cos(πx), which is continuous and periodic with period 2. Also, we have ∫0^2 cos(πx)dx = 0. Therefore, we can apply the test for convergence and write:
∫19^∞cos(πx)dx = ∫19^(19+2) cos(πx)dx + ∫(19+2)^(19+4) cos(πx)dx + ∫(19+4)^(19+6) cos(πx)dx + ...
= ∫0^2 cos(πx)dx + ∫0^2 cos(π(x+2))dx + ∫0^2 cos(π(x+4))dx + ...
= ∑n=0^∞ ∫0^2 cos(π(x+2n))dx
Since ∫0^2 cos(π(x+2n))dx = 0 for all n, the improper integral converges by the test for convergence.
Therefore, ∫19^∞cos(πx)dx converges, and its value is equal to 0.
The improper integral in question is:
∫(19 to ∞) cos(πx) dx
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An artist draws a square chalk mural with side length a. The artist decides to enlarge the mural. The area of the new mural is represented by (5a)(3a + 2).
Simplify the expression (5a)(3a + 2).
8a + 2
15a2 + 10a
15a2 + 10
8a2 + 10a
The expression (5a)(3a + 2) simplifies to 15a^2 + 10a. This is obtained by multiplying 5a with both terms inside the parentheses using the distributive property. The final result cannot be further simplified. So, Option B is correct. Option B.
To simplify the given expression, (5a)(3a + 2), we apply the distributive property to distribute the factor 5a to both terms inside the parentheses. This involves multiplying 5a by each term separately.
First, we multiply 5a by 3a. Multiplying these two terms gives us 15a^2, where the coefficient 15 comes from multiplying 5 by 3 and the variable a is squared due to the multiplication of two a's.
Next, we multiply 5a by 2. This multiplication results in 10a, where the coefficient 10 comes from multiplying 5 by 2, and the variable a remains unchanged.
Combining the two simplified terms, we have 15a^2 + 10a. This expression cannot be further simplified because there are no like terms to combine.
The term 15a^2 represents the enlarged area of the mural, obtained by multiplying the lengths of the sides of the original square mural (side length a) by the factor 5 and squaring the variable a. The term 10a represents an additional area added during the enlargement process, obtained by multiplying the side length a by the factor 2.
In conclusion, the simplified form of (5a)(3a + 2) is 15a^2 + 10a. So OptioN B is correct.
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a school counselor wants to compare the effectiveness of an online sat preparation program with an in-person sat preparation class. for an experiment, the counselor recruits 30 students who have already taken the sat once. the response variable will be the improvement in sat score. select all true statements. the completely randomized design is preferred the completely randomized design is better because it eliminates bias by considering all students to be equal at the start of the experiment. the matched pair design is preferred students who did not score well the first time they took the exam may benefit greatly from the class. by matching students by initial score, we can account for the variability in improvement that is introduced by the variability in student ability, making it easier to determine which program is more effective. students who scored well on the exam initially may not have much room for improvement even if the treatments are effective.
The correct statements for comparing the effectiveness of the SAT preparation program are the 3rd, 4th, 5th, 6th statements.
The statements in order are
The completely randomized design is preferredThe completely randomized design is better because it eliminates bias by considering all students to be equal at the start of the experimentThe matched pair design is preferredStudents who did not score well the first time they took the exam may benefit greatly from the classBy matching students by initial score, we can account for the variability in improvement that is introduced by the variability in student ability, making it easier to determine which program is more effectiveStudents who scored well on the exam initially may not have much room for improvement even if the treatments are effectiveSince, school counselor want to compare effectiveness of SAT preparation program with response variable will be the improvement in SAT score.
We can consider this as a improvement assessment, so that the initial abilities of each student will be different. With this we can see the improvement from student with bad initial score, and for the student that has a good score in initial exam they barely to have improvement.
For example student A have initial score 600 and student B have initial score 1300 after preparation program student A have final score 1200 and student B have final score 1350. In the example, we can see 200% improvement from student A and only 4% improvement from student B.
Also, with matching pair design that based on variable, we can see the variability in improvement making it easier to know the effectiveness of SAT preparation program than the randomized design.
Thus, the correct statements is the 3rd, 4th, 5th, 6th statements.
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Students were asked to choose their favorite food.
If 4/10 the students chose pizza and 4/10 chose tacos,
what fraction chose either pizza or tacos?
Answer:
4/5
Step-by-step explanation:
Simply add the two fractions together
4/10 + 4/10 = 8/10
Then simplify
8/10 = 4/5
4/5 students chose either pizza or tacos
Help The question is in the picture
Answer:
8h
Step-by-step explanation:
On a treasure map, the actual distance varies
directly to the scaled distance. If 15 actual
miles is represented by 3 centimeters on the
map, then how many centimeters on the map
are equivalent to 135 actual miles?
(A) 27 centimeters
(B) 32 centimeters
(C) 529 centimeters
(D) 675 centimeters
Answer:
Step-by-step explanation:
10 actual miles 2 cm 120 actual miles
What is the product?
(-2d^2+s)(5d^2-6s)
The answer is −10d4+17d2s−6s2
evaluate the expression 6x + 4 9/10 when x = 2/3.
x=2/3
6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10
Answer:
2x-1=y,2y+3=x
Step-by-step explanation:
no explanation
A card is drawn from a well shuffled pack of 52 cards. Find and match the probability of:
A 2 of Spades 1/13
A Jack 1/26
A red King 1/4
A Diamond suit 1/52
2 of Spades: There's only one 2 of spades card in the deck, so the probability of choosing the 2 of spades is 1/52.
A Jack: There are 4 Jacks in the deck, so the probability of choosing a jack is 4/52, or 1/13.
A red King: There are 2 red kings in the deck, so the probability of choosing one is 2/52, or 1/26.
A Diamond suit: There are 13 diamond cards in the deck, so the probability of choosing one is 13/52, or 1/4.
State whether the variable is discrete or continuous i) The number of cups of coffee sold in a cafeteria during lunch ii) The blood pressures of a group of students the day before their final exam 2. In a recent survey 76% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen at random, find the probability that exactly 8 of them favor the building of the police substation 3. The probability that an individual is left-handed is 0.15. In a class of 50 students, what is the mean and standard deviation of the number of left handers in the class?
1) (i)The number of cups of coffee sold in a cafeteria during lunch is discrete data.
ii) The blood pressure of a group of students the day before their final exam is continuous data.
2) The probability that exactly 8 of them favor the building of police substation 3 is 0.0639.
3) The mean and standard deviation of the number of left-handers in the class is 7.5 and 2.524.
What is the probability?
A probability is a number that reflects how likely an event is to occur. It is expressed as a number between 0 and 1, or as a percentage between 0% and 100% in percentage notation. The higher the likelihood, the more probable the event will occur.
Here, we have
Given: In a recent survey 76% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen at random, find the probability that exactly 8 of them favor the building of the police substation 3.
we have to find the mean and standard deviation of the number of left-handers in the class.
1)
i) The number of cups of coffee sold in a cafeteria during lunch is discrete data.
ii) The blood pressure of a group of students the day before their final exam is continuous data.
2) We have
n = 14 p = 0.76
using a binomial to find the following probability
P(X = 8) = ¹⁴C₈0.76⁸(1-p)⁶
P(X=8) = 0.0639
3)
Given n = 50 p = 0.15
we know the mean and standard deviation of binomial distribution
mean = n× p = 50×0.15 = 7.5
standard deviation = √(n×p×(1-p)) = √(50×0.15×0.85)
= 2.524
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Avery and Carmen both have summer jobs Avery gets paid $360 every four weeks, and gets paid $480 every six weeks summer break lasts a total of 12 weeks who earn more money during summer break every earns dollars per week Carmen earns dollars per week
Answer:
Avery earns $1,080 during summer
Avery weekly earnings = $1,080 / 12
= $90
Carmen earns $960 during summer
Carmen weekly earnings = $960/12
= $80
Carmen earns more money during summer break
Step-by-step explanation:
Avery payment = $360 every four weeks
Carmen payment = $480 every six weeks
summer break lasts a total of 12 weeks
Avery pay during summer = Total summer break weeks / 4 weeks × payment per 4 weeks
= 12 / 4 × $360
= 3 × $360
= $1,080
Carmen pay during summer = Total summer break weeks / 6 weeks × payment per 6 weeks
= 12 / 6 × $480
= 2 × $480
= $960
Avery earns $1,080 during summer
Avery weekly earnings = $1,080 / 12
= $90
Carmen earns $960 during summer
Carmen weekly earnings = $960/12
= $80
Carmen earns more money during summer break
Answer:
Step-by-step explanation:
Avery earns $1080 in 12 weeks
Carmen earns $960 in 12 weeks
Earpods are originally priced at $55 are marked down 20% off. What is the sale price?
Answer:
$44
Step-by-step explanation:
og $55
20% off
55 (starting number) x .20 (price off) = 11
55-11=44
A firm experiences_______ if inputs are doubled and output more than doubles. diminishing marginal rate of technical substitution diminishing marginal product decreasing returns to scale increasing returns to scale
A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.
When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.
The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.
This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.
The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.
Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.
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Elliott Farms has a silo for storage. The silo is a right circular cylinder topped by a right circular cone, both having the same radius. The height of the cone is half the height of the cylinder. The diameter of the base of the silo is 10 meters and the height of the entire silo is 27 meters. What is the volume, in cubic meters, of the silo
the volume of the silo is approximately 11,657.88 cubic meters.
To find the volume of the silo, we need to calculate the volumes of the cylinder and the cone separately, and then add them together.
The radius of the base of the silo is half the diameter, so it's 10 meters / 2 = 5 meters.
The height of the cylinder is given as 27 meters. Since the height of the cone is half the height of the cylinder, the height of the cone is 27 meters / 2 = 13.5 meters.
The volume of a cylinder is calculated using the formula:
Volume of Cylinder = π * radius^2 * height
Plugging in the values, we get:
Volume of Cylinder = π * 5^2 * 27 = 3375π cubic meters (approximately 10,598.07 cubic meters)
The volume of a cone is calculated using the formula:
Volume of Cone = (1/3) * π * radius^2 * height
Plugging in the values, we get:
Volume of Cone = (1/3) * π * 5^2 * 13.5 = 337.5π cubic meters (approximately 1059.81 cubic meters)
Adding the volumes of the cylinder and the cone, we get:
Volume of Silo = 3375π + 337.5π = 3712.5π cubic meters (approximately 11,657.88 cubic meters)
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find the minimum of the data set.
Answer:
23,600.
Step-by-step explanation:
23|6
An item sells for $75 and is on sale for 35% off. The sales tax is 9.8%. What is the final cost of the item?
The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.
The given problem is related to percentage discounts and sales tax and can be solved using the following steps:
Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25
Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75
Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79
Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.
Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54
Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!
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At Lincoln High School, 6 students are members of both the Chess Club and the Math Club. There are 20 students in the Math Club, 12 students in the Chess Club, and 400 students in the entire school. Find the probability that a student chosen at random belongs to the Chess Club or the Math Club
The probability that a student is chosen at random belongs to the Chess Club or the Math Club is 0.065.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes6 students are members of both the Chess Club and the Math Club.
There are 20 students in the Math Club, 12 students in the Chess Club, and 400 students in the entire school.
The probability that a student is chosen at random belongs to the Chess Club P(C) = 12/400
The probability that a student is chosen at random belongs to the Math Club P(M) = 20/400
The probability that a student is chosen at random belongs to both the Chess Club and the Math Club
P(C ∪ M) = 6/400
The probability that a student chosen at random belongs to the Chess Club or the Math Club
P(C ∩ M) = P(C) + P(M) - P(C ∪ M)
= 12/400 + 20/400 - 6/400
= 26/400
= 0.065
The answer is P(C ∩ M) = 0.065
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hey what's the answer
Liliflim pls answer this if u know !
pls with full explanation
Answer:
I hope the above attachment helps you mate
Have a great day
\(#Liliflim\)
Answer:
Solution given;
a⁴-23a²b²+b⁴
making in the form of a²+2ab+b²
a⁴+2a²b²+b⁴-2a²b²-23a²b²
(a²+b²)²-(5ab)²
factoring by using formula
x²-y²=(x+y)(x-y)
(a²+5ab+b²)(a²-5ab+b²)
2. sophia is considering buying a dress and a necklace. the probability she will buy a red dress is 0.2, and similarly, it is 0.4 for a blue dress. there is a 10% chance she will buy a necklace. she wants to buy at most one dress, and buying a necklace is independent of buying a dress find the probability she buys at least one of the previous items. assume event a: she buys a red dress; event b: she buys a blue dress; event c: she buys a necklace.
Therefore the probability that she buys at least one of the previous items is 0.1333
What is probability ?The area of mathematics known as probability deals with numerical descriptions of the likelihood that an event will occur or that a statement is true .A number between 0 and 1 is the likelihood of an event, where, broadly speaking, 0 signifies the event's impossibility and 1 denotes its certainty.
Given:
event A: she buys red dress.
event B: she buys a blue dress.
event C: she buys a necklace.
the probability she will buy a red dress is 0.2,
the probability she will buy a blue dress is 0.4
there is 10% chance she will buy a necklace =0.10
The probability she wants to buy at most one dress,
P(A or B or C) =0.2 +0.4 +0.1 -(0.08 -0.04 -0.02 +0.08)
P(A or B or C) =0.568
the probability she buys at least one of the previous items is
\(\frac{P(A or B or C)}{P(AorB andC)}\) = \(\frac{0.2 * 0.1 * 0.4}{(0.2 * 0.1)+(0.1 *0.4)}\)
\(\frac{P(A or B or C)}{P(AorB andC)}\)= 2/15 =0.133
Therefore the probability that she buys at least one of the previous items is 0.1333
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The distance between San Jose, California, and Las Vegas, Nevada, is about 375 miles. The distance from Las Vegas to Carlsbad, California, is about 243 miles. Use the Triangle Inequality Theorem to find the possible distance between San Jose and Carlsbad. (Lesson 5-3)
The possible distance between San Jose and Carlsbad is between 132 miles and 618 miles.
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we can consider a triangle with sides representing the distances between San Jose, Las Vegas, and Carlsbad.
Given:
Distance between San Jose and Las Vegas: 375 miles
Distance between Las Vegas and Carlsbad: 243 miles
To find the possible distance between San Jose and Carlsbad, we need to consider the sum of these distances. Using the Triangle Inequality Theorem, we have:
375 + 243 > x
Simplifying the inequality, we get
618>x
So, we can also consider:
375 - 243 < x
Simplifying the inequality, we get:
132 < x
This means that the possible distance between San Jose and Carlsbad must be greater than 132 miles.
Combining both inequalities, we can conclude that the possible distance between San Jose and Carlsbad is between 132 miles and 618 miles, inclusive.
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The number of users on a website is 6700 and is growing exponentially at a rate of 79% per year. write a function to represent the number of users on the website after t years, where the daily rate of change can be found from a constant in the function. round all coefficients in the function to four decimal places. also, determine the percentage rate of change per day, to the nearest hundredth of a percent.
To represent the number of users on the website after t years, we can use the exponential growth function. Let's break down the problem step by step. The initial number of users on the website is 6700. This is our starting point.
The growth rate is given as 79% per year. To convert this into a decimal, we divide it by 100: 79% = 0.79. Now, we need to write the exponential growth function. Let N(t) represent the number of users on the website after t years. The function can be written as follows: N(t) = N(0) * (1 + r)^t Where N(0) is the initial number of users (6700), r is the growth rate (0.79), and t is the number of years. Plugging in the values, the function becomes N(t) = 6700 * (1 + 0.79)^t
To round the coefficients in the function to four decimal places, we need to apply the rounding rule. If the fifth decimal place is greater than or equal to 5, we round up the fourth decimal place. Otherwise, we leave the fourth decimal place as it is. Finally, let's determine the percentage rate of change per day. To do this, we can divide the annual growth rate by the number of days in a year (365) and multiply by 100 to convert it into a percentage. And the percentage rate of change per day is approximately 0.216%.
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What is the length of the diameter of the circle defined by the equation x^(2)-8x+y^(2)-4y+12=0 ? Round off your answer to the nearest hundrec answer has more than 2 decimal places.
The length of the diameter of the given circle x² - 8x + y² - 4y + 12 = 0 is 5.66 units.
We use the concepts of circles in 2-D Coordinate Geometry to find the diameter of the circle as required.
On the x-y plane, the general form of the equation of a circle is defined as:
x² + y² + 2gx + 2fy + c = 0
where,g,f, and c are constants.
But this equation can be used to derive a few more parameters relating to the circle, such as:
The center of a circle is (-g , -f).
The radius of the circle is √(g² + f² - c)
So, for the given circle,
x² - 8x + y² - 4y + 12 = 0
g = -4 , f = -2 and c = 12
From these, the radius has a value of:
r = √[ (-4)² + (-2)² - 12 ]
r = √[ 16 + 4 - 12]
r = √8
r = 2√2 units.
From the radius, we're one step away from the diameter.
d = 2r = 2 * 2√2
d = 4√2 units ≈ 5.656
Thus, the diameter of the required circle is 5.656 units.
According to the rounding-off mentioned, the diameter is 5.66 units.
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2. The volume of a 3-D shape is 13 cubic feet. The shape is scaled up and the new volume is 832 cubic
feet. What was the scale factor?
Scale factor of given equation is 64 : 1
What is scale factor ?Scale Factor is used to scale the shape in various dimensions. In Geometry you will learn about different geometric shapes in 2D and 3D. A scale factor is a measure of similar figures that look the same but have different scales or measurements. Suppose two circles are similar but may have different radii. The scale factor indicates how much larger or smaller the figure is than the original figure. Scale allows you to scale the original shape up or down and draw it. The amount by which a shape is magnified or shrunk is called the scale factor. Used when you need to increase the size of 2D shapes such as circles, triangles, squares, and rectangles. Magnification is also well understood from the basic theorem of proportionality.Calculationinitial volume = 13 cubic feet
final volume = 832 cubic feet
scale factor = 832 / 13
= 64 : 1
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Solve For X. Solve similar triangles (advanced)
The value of x in the given similar triangles ADB and BCE is 4.5.
To solve for x in the given similar triangles ADB and BCE, we can set up the proportion of corresponding sides:
In triangle ADB, we have:
AB/BD = x/DE
Substitute the given values:
3/4 = x/6
Now, cross-multiply and solve for x:
3 * 6 = 4x
18 = 4x
x = 18/4
x = 4.5
So, the value of x is 4.5.
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I’m not sure I need help
Answer:
D) \(1 < x\leq 4\)
Step-by-step explanation:
1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)
Shawna is making smoothies. The recipe calls for two parts yogurt to three parts blueberry. Shawna wants to make 10 cups of smoothie. Mix how many cups of yogurt and blueberries does Shawna need
Answer:
Shawna needs a mix of 4 cups of yoghurt and 6 cups of blueberries
Step-by-step explanation:
Here, we want to know the number of cups of yoghurt and smoothies Shawna needs to make;
We have 2 parts yoghurt and 3 parts blueberry, so we can say we have a ratio of 2:3
The total number of cups to be made is 10
So the number of cups of yoghurt will be;
2/(2+3) * 10
= 2/5 * 10 = 4 cups
The number of cups of blueberry would be;
3/5 * 10 = 6 cups
So a mix of 4 cups of yoghurt and 6 cups of blueberries is needed by Shawna
Can you please help me thank you so much I really appreciate it if you up
Answer
$12.41
Step-by-step explanation
1 pound is equivalent to $0.85 in the shipping fee.
To find the shipping fee equivalent to 14.6 pounds, we can use the next proportion:
\(\frac{1\text{ pound}}{14.6\text{ pounds}}=\frac{0.85\text{ \$}}{x\text{ \$}}\)Cross-multiplying and omitting the units:
\(\begin{gathered} 1\cdot x=0.85\cdot14.6 \\ x=\text{ \$}12.41 \end{gathered}\)Thunder from a bolt of lightening travels 1/10 mile in ½ second. At this rate, how many miles can it travel in one second?
Step-by-step explanation:
it could travel 2/10 of a mile in one second because 1/10 ×2 =2/10
Answer:
1/5
Step-by-step explanation:
1/10*2=2/10=1/5
5(1+n)=-5 someone help!!!!!!!!!!!
Answer: -2
Step-by-step explanation:
-Distribute : 5+5n=-5
-Set both sides : 5n=-10
-Divide : -10/5n = -2