Sloan is going to make a berry salad for a party.
Her salad will include only blueberries, raspberries, and strawberries. She wants the ratio of blueberries to strawberries to be 2:5, and the ratio of blueberries to all berries to be 4:23. How many of each type of berry can she put in the salad?

Answer:

Step-by-step explanation:

The average rate of change of a function over an interval is equal to the total change in the function's output divided by the total change in the input over the interval. In other words, it is the slope of the secant line that connects the two points on the function defined by the interval.

If the function is represented by y = f(x), the average rate of change of the function over the interval [-4, -3] can be calculated as:

Δy / Δx = (f(-3) - f(-4)) / (-3 - (-4))

So, to calculate the average rate of change, you would need to know the values of the function f(x) at x = -3 and x = -4. If you provide the equation for the function f(x), I can help you find the average rate of change.

The number of tons required when the central HVAC unit will be installed is 1. 73 tons

For the HVAC unit to be installed, the three separate incubation rooms will have to be installed.

This means that the tons required for the central HVAC unit would be the total sum of the three requirement for the other incubation rooms.

The sum would be :

= 1 / 5 + 5 / 6 + 25 / 36

= 0. 2 + 0. 8333 + 0. 69444

= 1. 72774

= 1. 73 tons

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The closest answer to initial value of the account is $538,021.66

It is given that the money Seth withdraws was compounded every quarter for 35 years. So, we get,

Amount withdrawn every quarter, P = $4567

Rate of interest, r  =  = 0.002525

Time period, n = 35 × 4 = 140

Now, as we know the formula for annuity as,

[tex]PV = PMT[(1 - (1 / ( 1 + r)^n)) / n][/tex]

where P = installments, PV = present value, r = rate of interest and n = time period.

This gives,[tex]PV = PMT[(1 - (1 / ( 1 + r)^n)) / n]= 4567[1 - (1 / 1.00253^40)) / 0.00253][/tex]

= 4567[(1 - 0.70254) / 0.00253]

= 4567[117.80636]

= $538,021.66

So, the closest answer to initial value of the account is $538,021.66

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The answers are given as follows:

2
a)

A = 8

b = 10

x = 118°

y = 62°

b)

a = 8

b = 15

y = 50

x = 100°

3)

(a)

∠2 = 25°

∠3 = 65°
∠4 = 65°
∠5 = 90°

(b)

since SL = 10,
i) LT  10
ii) TM = 10

iii) SM = 10

4)

a) Since m∠118
∠2 = 18°
∠3 = 72°
∠4 = 72°

If FA = 27, then LO = 13.5

The above are resolved using the properties of Parallelograms; Rhombus, and Rectangle

Since the above answers are justified by the qualities or properties of :

Parallelograms; Rhombus, and Rectangle, lets look at them one by one.

2
a)

A = 8 - opposite sides of a parallelogram are equal in length

b = 10 -opposite sides of a parallelogram are equal in length

y = 62° - opposite angles of a parallelogram are of equal measure.

x = 118° - Sum of angles of a parallelogram - 360°. x = (360 - (62*2))/2

= 118°

3)

(a) Here we have a Rhombus.

∠2 = 25° - Opposite angles of a rhombus are equal; Diagonals bisect the angles of a rhombus. Thus ∠1≅∠2

∠3 = 65° - Since diagonals bisect each other at right angles, ∠3 = 180 - (25+90) = 65°
∠4 = 65° - Diagonals bisect the angles of a rhombus. Thus, ∠3≅∠3
∠5 = 90° - [properties of a Rhombus]

(b)

since SL = 10,
i) LT  10 - All sides of a Rhombus are equal
ii) TM = 10 - All sides of a Rhombus are equal

iii) SM = 10 - All sides of a Rhombus are equal


4) Here we have a Rectangle.

a) Since m∠18
∠2 = 18° because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠2≅∠1 (AAS)
∠3 = 72° - Each interior angle is equal to 90 degrees. Thus, m∠ =  90-18 = ∠72°
∠4 = 72° - because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠4≅∠3(AAS)

If FA = 27, then LO = 13.5 - The diagonals bisect each other.Thus,

LO = FA/2

LO = 27/2

LO = 13.5

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The most likely explanation for the inconsistency between the first and second studies is that the initial findings were a false positive, meaning that the effect observed was not actually present in the population being studied.

In the given scenario, the researcher tested a new laparoscopic treatment for chronic shoulder dislocation and found statistically significant results compared to an older treatment. This means that the difference between the two treatments was not due to chance and is likely to be a real effect.

However, a replication study failed to show statistical significance, which means that the difference between the two treatments could have been due to chance. This can happen even if the sample sizes were sufficient in all four studies. A lack of statistical significance in a replication study indicates that the effect observed in the first study may not be as strong or consistent as previously thought.

The fact that the third and fourth studies produced the same effects as the second could be attributed to random variation or other factors such as study design, sample selection, or measurement methods.

Statistical significance is a crucial concept in research as it helps to establish the credibility of a study's findings. However, it is important to understand that statistical significance alone does not necessarily mean that the effect observed is meaningful or important in practical terms.

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The equation connecting y and x when y is directly proportional to x and y = 30 when x = 6 is y = 5x.

If y is directly proportional to x, we can write the equation in the form:

y = kx

where k is the constant of proportionality.

To find k, we can use the values of y and x given:

y = 30, x = 6

When we enter these values into the formula above, we obtain:

30 = k * 6

Solving for k, we get:

k = 30/6 = 5

Therefore, the equation connecting y and x when y is directly proportional to x is:

y = 5x

When two variables are directly proportional, it means that when one variable increases or decreases, the other variable changes in the same proportion. In this scenario, we are given that y is directly proportional to x and we are also given a specific point on the line, (6, 30). Using this information, we can solve for the constant of proportionality k and write the equation connecting y and x as y = kx, where k is 5.

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Answer:

C 11

Step-by-step explanation:

you have 1 less penny than dimes which is 10 pennies

you have 2 less nickels than dimes which is 9

11+10+9=30

The exponential equation is y=2,642(2.5)ˣ. x represents the number of days.

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

Given that a video was released to the public, it already had 2,642 views.

One day later, the number of views increased to 3,963.

The number of viewers after one day is ( 3,963 + 2,642 ) = 6,605

Assume that the exponential function y = a(b)ˣ represents the number of viewers. x represents the number of days.

Putting x = 0 and  y = 2,642 in y = a(b)ˣ:

2,642 = a(b)⁰

a = 2,642

Putting x = 1 and  y = 6,605 in y = a(b)ˣ:

6,605 = a(b)¹

Putting a = 2,642:

6,605 = 2,642(b)¹

b = 6,605/2,642

b = 2.5

Therefore, an exponential equation is y=2,642(2.5)ˣ.

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The solution of the given system of linear equations is (1, -1)

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given is a system of linear equations, x - 3y = 4 and y = -3x + 2, we need to find the point which is the solution of the system,

The linear equations are :-

x-3y = 4...(i)

y = -3x+2....(ii)

Put eq(ii) in eq(i)

x-3(-3x+2) = 4

x+9x-6 = 4

10x = 10

x = 1

Put x = 1 in eq(ii)

y = -3+2

y = -1

Therefore, the solution point is (1, -1)

We can find the solution point by graphing method also, we will plot the graph of the lines and the line where intersects is the solution point is (1, -1) [attached]

Hence, the solution of the given system of linear equations is (1, -1)

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The complete question is (Multiple Choice Worth 2 points)

(Systems of Linear Equations MC)

Which point is a solution of the system of linear equations?

x - 3y = 4

y = -3x + 2

A) (9,0)

B) (-5, 8)

C) (1, 1)

D (1, -1)

Answer:

c=8p

Step-by-step explanation:

c=8p

The number of which 3.92 is 56 percent, is 7.

A percentage of an object is how many parts of it there are out of 100 equal parts. For example, if you split a shape into 100 parts, 20 of the parts make 20%.

Given that, 3.92 is what number's 56%,

Let the number be x,

Therefore, by the definition of percentage,

56% of x = 3.92

56/100 × x = 3.92

x = 3.92 × 100/56

x = 392/56

x = 7

Hence, the number of which 3.92 is 56 percent, is 7.

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Answer:

x = 40.5

Step-by-step explanation:

SQ is an angle bisector and divides the opposite side into segments that are proportional to the other two sides, that is

[tex]\frac{PS}{RS}[/tex] = [tex]\frac{PQ}{RQ}[/tex] ( substitute values )

[tex]\frac{20}{18}[/tex] = [tex]\frac{45}{x}[/tex] ( cross- multiply )

20x = 18 × 45 = 810 ( divide both sides by 20 )

x = 40.5

The five number summary is the minimum, first quartile (25th percentile), median (50th percentile), third quartile (75th percentile), and the maximum.

To give the smallest interval that we know contains the 30th percentile, we would take the 25th percentile and the 30th percentile. So, the smallest interval that we know contains the 30th percentile would be [25th percentile, 30th percentile].

The smallest interval that contains the 30th percentile is [25th percentile, 30th percentile], which is found using the five number summary (minimum, first quartile, median, third quartile, and maximum).

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The function that can be used to find the total height, h, of the building in feet, including the antenna is h = 6.8n + 13.5.

A builder is constructing an office building with n floors that will have an antenna 13.5 feet tall on its roof. Each floor of the building will be 6.8 feet high.

Therefore, the function that can be used to find the total height of the building in feet including the antenna can be calculated as follows:

Therefore,

n = numbers of floors in the building.

h = total height of the building

Hence, the function is as follows

h = 6.8n + 13.5

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Answer:

Step-by-step explanation:

... good luck

The number in question is the magic sum of the square. The outcome is the same as if you multiply the three integers in each column together and then add the three products: 8, times 3, 4, 1, 5, 6, 7, and 2 equals 225. This quantity is known as the magic square product.

The term "integer" refers to any number that is not zero, a positive natural number, or a negative integer denoted by a minus sign. Because they are diametrically opposed to their positive counterparts, negative integers are additive.

When representing a group of numbers in mathematical notation, the blackboard bold mathbb Z or boldface Z are frequently used. The word "integer" is pronounced "IN-tuh-jer" and refers to a whole number that can be positive, negative, or zero.

A few examples of integers are -5, 1, 5, 8, 97, and 3,043. Non-integer numbers include the figures -1.43, 1 3/4, and 3.14.

The integers are a collection of all whole numbers and their antipodes. Decimal points and fractions are not included in the set of integers. The numbers 2, 5, 0, 12, 244, 15, and 8 are examples.

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For the given data, the cutoff point using the upper fence is 791.25 minutes.

To find the cutoff point using the upper fence, we need to first calculate the lower and upper fences.

The lower fence is given by the formula:

Lower fence = Q1 - 1.5 x IQR

where Q1 is the first quartile and IQR is the interquartile range.

The upper fence is given by the formula:

Upper fence = Q3 + 1.5 x IQR

where Q3 is the third quartile and IQR is the interquartile range.

To find these values, we first need to order the data:

307 311 322 321 354 363 377 406 410 425

435 461 464 474 499 505 513 534 548

The first quartile (Q1) is the median of the lower half of the data:

Q1 = (354 + 363) / 2 = 358.5

The third quartile (Q3) is the median of the upper half of the data:

Q3 = (513 + 534) / 2 = 523.5

The interquartile range (IQR) is the difference between the third and first quartiles:

IQR = Q3 - Q1 = 523.5 - 358.5 = 165

Now we can calculate the lower and upper fences:

Lower fence = Q1 - 1.5 x IQR = 358.5 - 1.5 x 165 = 91

Upper fence = Q3 + 1.5 x IQR = 523.5 + 1.5 x 165 = 791.25

Therefore, the cutoff point using the upper fence is 791.25 minutes. Any customer who uses more than 791.25 minutes in a month should be contacted by the phone company as part of the fraud prevention program.

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Answer: There would be a higher rate on the 2250 labels on 150 sheets.

Step-by-step explanation:

1080/90 = 12

2250/150 = 15

There would be a higher rate on the 2250 labels on 150 sheets.

By using line of best fit, the time for a trip of 6 miles long is 11.96 minutes.

A line of best fit is a graphical representation of straight line which gives  the best approximation of the given data set.

A taxi driver records the time required to complete various and the distance for each trip.

The best-given fit line by the equation y=0.467x + 0.417.---(1)

where y represents the distance miles, and x represents the time for the trip in minutes.

To find the time for a 6 miles:

i.e., substitute y=6 in the equation(1)

6=0.467x+0.417

⇒x=11.96 minutes.

Hence, by using line of best fit, the time for a trip of 6 miles long is 11.96 minutes.

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The transformation that is used to transform the figure P to figure Q is described by (b) (x, y) → (x+5, y+3).

The Transformation of the "figure P" being translated 5 units to the right and 3 units up to create the "figure Q" is called as a type of "translation" in the coordinate plane.

When we shift a point (x, y) by "a" units to the right and "b" units up, the new coordinates become as ⇒  (x + a, y + b).

The coordinates of "figure P" is translated 5 units to the right and 3 units up, that means we will use the rule (x,y) → (x+5, y+3) to describe the transformation.

Therefore, the correct transformation used is  (b) (x, y) → (x+5, y+3).

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The given question is incomplete , the complete question is

A "figure P" was translated 5 units to the right and 3 units up to create "figure Q". Which rule describes this transformation ?

(a) (x, y) → (x-5, y-3)

(b) (x, y) → (x+5, y+3)

(c) (x, y) → (x-3, y-5)

(d) (x, y) → (x+3, y+5)

240

Step-by-step explanation:

12-8+4+[(6+2)-3]2×3

= 4+4[(6+2)-3]2×3

= 8[(6+2)-3]2×3

= 8[(8)-3]2×3

= 8[5]2×3

= 8[5]6

= 40(6)

= 240

Answer:

C

Step-by-step explanation:

This would represent the point (0,3)  You would move 5 units to the right of where x is 5.

The multiply of 45 and 23 is = 1035  we calculate this by simple multiplication method.

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

And here we have 2 number 1st is 45 and 2nd is 23 so here we will multiply

    4  5

 x  2 3

----------------

  1 3 5

  9 0 x

---------------

1 0 3 5

--------------

final ans is 1035

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Mr. Durant has 5.75 acres of lawn, therefore he was charged $125

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

The slope intercept form of an equation is:

y = mx + b

where m is the rate of change and b is the y intercept.

Let y represent the total cost of charging  for mowing x acres.

He charges a flat rate of $10 plus $5 per quarter acre of lawn. Therefore:

$5 = quarter acre; $(5 * 4) = $20 is for one acre.

y = 20x + 10

He made a total of $125; hence:

125 = 20x + 10

115 = 20x

x = 5.75 acres

Mr. Durant has 5.75 acres of lawn.

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The scale to figure out the heavier stack 2 gram higher.

To determine the heavier stack of coins, you will need to use the electronic scale. However, since you cannot weigh all the coins at once, you will have to use the concept of unitary method.

Based on this, you can calculate the total weight of the coins on the scale. Since each coin weighs 1 gram, the total weight of the coins should be equal to the sum of the natural numbers from 1 to 10, which is 55.

Next, you need to compare the weight of the coins on the scale to the expected weight of 55 grams. If the weight on the scale is less than 55 grams, then the stack of coins that you did not weigh is the heavier stack.

However, if the weight on the scale is more than 55 grams, you need to use the concept of unitary method again. Suppose the weight on the scale is 56 grams. This means that the heavier stack has one coin that weighs 2 grams, and the other stack has 10 coins that weigh 1 gram.

To determine which stack is heavier, you can subtract the expected weight of 55 grams from the weight on the scale (56 grams). The difference is 1 gram.

Now you need to divide the difference by 2 (since one coin weighs 2 grams). This gives you 0.5. This means that the heavier stack has 0.5 coins that weigh 2 grams.

Since you cannot have half a coin, this means that the stack with one coin that weighs 2 grams is the heavier stack.

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The ratio of girls to boys in the class is 1:3, meaning that for every one girl there are three boys.

There are 10 girls and 30 boys in the class.

The ratio of girls to boys can be expressed as a fraction: 10/30.

To make the fraction easier to understand, we can simplify it to its lowest form: 1/3.

The ratio of girls to boys in the class is therefore 1:3, meaning that for every one girl there are three boys.

The ratio of girls to boys in a class can be determined by dividing the number of girls by the number of boys. In this case, there are 10 girls and 30 boys, so the ratio is 10/30. This fraction can be simplified to its lowest form, 1/3. This means that for every one girl there are three boys in the class. Knowing the ratio of girls to boys can be helpful in a variety of situations, such as organizing activities or determining the number of supplies needed. This ratio can also be expressed as a percentage, with 10% of the class being girls and 30% being boys. Knowing the ratio of girls to boys can also be a useful tool in understanding the demographics of the class.

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Answer:

x = 8

Step-by-step explanation:

AB/AC = BD/DC

2x/12 = x+4/x+1

12x + 4 = 2x² + 2x

2x² - 10x - 48 = 0

x² - 5x - 24 = 0

(x-8) (x+3) = 0

x = 8 (or) x= -3 (impossible)

x = 8

Answer:

Tje answer is 36

Step-by-step explanation:

16-30=14

24+14=-36