During a bake sale, 5 ¾ dozen cookies were sold in ⅓ hour. What is the unit rate for the dozens of cookies sold per hour?

To find the scalar projections, uv and vu, we must first find the magnitude of each vector and the angle between the vectors.

The magnitude of vector u is sqrt\((2^2 + 1^2) = sqrt(5)\) and the magnitude of vector v is \(sqrt(4^2 + (-1)^2) = sqrt(17)\). The angle between the vectors is given as 40 degrees.Using the formula for the scalar projection of u onto v, we get: uv = (u . v)/|v|, where u . v is the dot product of u and v.u . v = (2)(4) + (1)(-1)

= 8 - 1

= 7uv

= \((7)/(sqrt(17))\)

≈ 1.33Using the formula for the scalar projection of v onto u, we get: vu = (v . u)/|u|, where v . u is the dot product of v and u.v . u

= (4)(2) + (-1)(1)

= 8 - 1

= 7vu

= (7)/(sqrt(5))

≈ 3.16

Therefore, uv = 1.33 and

vu = 3.16

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Answer: $1,560

Step-by-step explanation:

Assume the computer's price is x.

This means that expressing the printer in terms of x would be:

= 30% * x

= 0.3x

These two put together represent the cost of $2,028

Expression is:

x + 0.3x = 2,028

1.3x = 2,028

x = 2,028/ 1.3

x = $1,560

Computer was $1,560

Printer was therefore:

= 1,560 * 30%

= $468

Answer:

8km

Step-by-step explanation:

The three points form a right-angled triangle with 15km as the height and 17km as the hypotenuse.

To find the distance between Lowell and the port which is the base use the pythagorean theorem.

=√17² - 15²

=8km

The length of the apothem of the regular triangle with a perimeter of 96√3 units is 16 units.

To find the length of the apothem of a regular triangle, we need to know the length of one of its sides. We are given the perimeter of the triangle, which is 96√3 units. Since a regular triangle has three equal sides, we can divide the perimeter by 3 to get the length of one side:

96√3 ÷ 3 = 32√3 units

Now, we can use the formula for the apothem of a regular triangle:

apothem = (side length) / (2 * tan(π/3))

where π/3 is the angle between the apothem and one side of the triangle (which is 60 degrees for a regular triangle).

Plugging in the values we have:

apothem = (32√3) / (2 * tan(π/3))

apothem = (32√3) / (2 * √3)

apothem = 16 units

Therefore, the length of the apothem of the regular triangle with a perimeter of 96√3 units is 16 units.

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To determine the minimum sample size needed for the researcher to be confident that his estimate is within "mm" hg of the true mean systolic blood pressure, we will use the following formula:

n = (Z * σ / E)²

where:
n = minimum sample size
Z = Z-score corresponding to the desired confidence level
σ = population standard deviation (in this case, "mm" hg)
E = margin of error (in this case, "mm" hg)

1. Determine the Z-score corresponding to the desired confidence level. Common confidence levels include 90%, 95%, and 99%, which correspond to Z-scores of 1.645, 1.960, and 2.576, respectively. Choose the appropriate Z-score based on the desired confidence level.

2. Substitute the given values of σ and E (both in "mm" hg) and the chosen Z-score into the formula: n = (Z * σ / E)²

3. Carry out the calculations, rounding the result up to the nearest whole number. This will ensure that the sample size is the minimum whole number that satisfies the requirements.

4. The result is the minimum sample size needed for the researcher to be confident that his estimate is within "mm" hg of the true mean systolic blood pressure.

Note: Since this question haven't provided specific values for standard deviation, margin of error, and desired confidence level . follow the steps with the specific values you have to find the minimum sample size.

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there will be 27 zeros at the end of 115!.

To determine the number of zeros at the end of 115!, we need to consider the prime factorization of the number and examine how many factors of 5 are present.

A zero at the end of a factorial occurs when there is a factor of 10 present, which is equivalent to having both factors of 2 and 5. Since the number of factors of 2 is usually abundant, the crucial factor is the number of factors of 5.

In the prime factorization of 115!, the factors of 5 arise from the multiples of 5 (5, 10, 15, 20, ...) as well as higher powers of 5 (25, 50, 75, ...). We need to determine how many multiples of 5, multiples of 25, multiples of 125, and so on are present.

1. Multiples of 5: The number of multiples of 5 in 115! is given by ⌊115/5⌋ = 23.

2. Multiples of 25: The number of multiples of 25 in 115! is given by ⌊115/25⌋ = 4.

3. Multiples of 125: The number of multiples of 125 in 115! is given by ⌊115/125⌋ = 0 since there are no numbers in the range 1 to 115 that are multiples of 125.

Adding up these counts, we have 23 + 4 = 27 factors of 5.

Therefore, there will be 27 zeros at the end of 115!.

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Answer: 80

Step-by-step explanation:

To solve this,we will use the formula for direct proportion which is:

y = kx

where k = number of cookies made = 24

x = time taken = 1.5 hours

Since y = kx

24 = 1.5k

k = 24/1.5

k = 16

Then, the amount of cookies that can she make in 5 hours will be:

y = kx

y = 16 × 5

y = 80

She can make 8 cookies in 5 hours.

Answer:

The probability that the individual has the disease is 1/500

Step-by-step explanation:

i found the fraction of 1 in 500 which is 1/500, hope this helps :)

Here are three ratios that are equivalent to 4:12: 1:3, 2:6, and 5:15.

To create ratios that are equivalent to 4:12, we need to find ratios with the same relative values. The ratio 4:12 can be simplified by dividing both numbers by their greatest common divisor, which is 4.

After simplifying, we get the ratio 1:3. This means that for every 1 part of the first quantity, there are 3 parts of the second quantity.

We can also multiply both numbers of the original ratio by the same factor to create equivalent ratios. Multiplying 4:12 by 2 gives us 8:24, which can be simplified to 2:6.

Similarly, multiplying 4:12 by 5 gives us 20:60, which can be simplified to 5:15.

Therefore, the three equivalent ratios to 4:12 are 1:3, 2:6, and 5:15.

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Answer:

Step-by-step explanation:

Given diameter of a beach ball is d=10 inches.Let us find the radius of the beach ball:d=2 r10=2×rr=102∴r=5Therefore, the radius of a beach is 5 inches.Let us find the volume of air contained inside the beach ball:V=43 π×r3=43 π×53=43 π×125=500π3∴V=523.59877Therefore, the volume of air contained inside the beach ball is approximately 523.6 in3.

Answer:

The formula for the volume of a sphere is:

V = (4/3)πr³

We can rearrange this formula to solve for the radius (r):

r = [(3V) / (4π)]^(1/3)

where V is the volume of the sphere.

Substituting the given volume of the beach ball, we get:

r = [(3 × 10,332 in³) / (4 × 3.14)]^(1/3)

r = 10.27 in

Rounding to the nearest tenth, the approximate radius of the beach ball is 10.3 inches.

Answer:

y=x-10

Step-by-step explanation:

y=ax+b - linear equation

y=-x+7

a=-1

y=cx+d - perpendicular equation to y=ax+b

a*c=-1

(-1)*c=-1

c=1

y=x+d

(4,-6) => x=4, y=-6

y=x+d => -6=4+d

d=-10

y=x-10

Answer:

B (2, 3)

The two lines intersect near that point.

Answer:

Step-by-step explanation:I don't say you must have to mark my ans as brainliest but my friend if it has really helped you plz don't forget to thank me...

The axis of symmetry of the graph of the quadratic function represented by the equation is x=-b/2a

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

The standard formula for a quadratic equation is expressed as

y=ax^2+bx+c

All quadratic functions have an axis of symmetry and they are expressed according to the equation  x=-b/2a

Hence the axis of symmetry of the graph of the quadratic function represented by the equation is  x=-b/2a

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Answer:

answer is  

A.21,369 or  D. 56,783

Step-by-step explanation:

am  not sure but am mostly sure it is D but i dont know i think is A to but am

99% is D

hope it helps

Answer:

Your answer is C 48,618

Step-by-step explanation:

if you add the sum up of all of the digits it is divisible by both three and nine.

can i plz get brainliest.

Answer:

See answers below

Step-by-step explanation:

Given the function:

f(x) = 0.15x + 900

a) f(80) = 0.15(80) + 900

f(80) = 12 +  900

f(80) = 912

b)  f(120) = 0.15(120) + 900

f(120) = 18 +  900

f(120) = 918

c) f(200) = 0.15(200) + 900

f(200) = 30 +  900

f(200) = 930

d)  f(56) = 0.15(56) + 900

f(56) = 8.4 +  900

f(56) = 908.4

Answer: Convert the mixed numbers to improper fractions, then find the LCD and combine.

Exact Form: −37/4

Step-by-step explanation:

Answer: 2

Step-by-step explanation: 10 minutes is 1/6 of an hour meaning that you would divide 12 by six to get your answer.

Trigonometric identity is Cos(α+β) = -1

The information given below to find cos (a+ß). For given data Cos(α+β)=-1 Trigonometric identity & Pythagoras theorem :

Pythagoras theorem is given by

              \(h^{2} = p^{2} +b^{2}\)

where,

               h = hypotenuse

               p = perpendicular

               b = base

Given,

tanα = 4/3 = p/b

    α in quadrant III

hypotenuse (h) = \(\sqrt{ (p^{2} + b^{2}) }\)

                       h  \(\sqrt{(4^{2} + 3^{2} )} \\\\= \sqrt{16 + 9} \\\\=\sqrt{25} \\\\= 5\)

In,

    III quadrant sinα and cosα both are negative.

    sinα = -4/5

   cosα = -3/5

Cosβ = 3/5 = b/h

   β in quadrant IV

Perpendicular can be calculated by using Pythagoras theorem,

\(p = \sqrt{h^2 - b^2}\\\\ = \sqrt{5^2 - 3^2}\\\\= \sqrt{25 - 9}\\\\= \sqrt{16}\\ \\= 4\)

In IV quadrant,

sinβ  is negative  and cosβ  is positive

sinβ = -4/5

Cos(α+β) = cosα . cosβ  -  sinα . sinβ

               = (-3/5)(3/5) - (-4/5)(-4/5)

               =  -9/25 -16/25

               = -25/25

               = -1

Thus,

          Cos(α+β) = -1

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Answer:

3:10

Step-by-step explanation:

3:10 is the ratio form of 3/10

Answer:

40

Step-by-step explanation:

\(m \angle 2=20^{\circ}\) (angle sum of triangle)

\(m\angle 1=40^{\circ}\) (angle sum of triangle)

Answer:

It would take 45 minutes to get 18 marks

Step-by-step explanation:

30 ÷ 12 = 2.5

2.5 x 18 = 45

It would take 45 minutes to get 18 marks

Answer:

AB = 48

AD = 7√2

Step-by-step explanation:

since AD - 26, DB = 26 and DC = 26

AE² = 26² - 10² = 676 - 100 - 576

AE = √576 = 24

AB = 2 x 24 = 48

If arc BC is 45°, then ∠BDC = 45°

AD² = 7² + 7² = 49 + 49 = 98

AD = √98 = 7√2

Answer:

  y = 3x -4

Step-by-step explanation:

The two pairs of x and y values are used to find the slope of the line. That and one of the pairs is used to find the y-intercept. These values are put into the slope-intercept equation to give the equation of the line through the two points.

__

Each (x, y) pair represents a point on a graph. The slope-intercept equation for a line relates all the (x, y) pairs that lie on the line. That equation is ...

  y = mx +b . . . . . . where m is the slope, and b is the y-intercept

The slope is the "steepness" of the line. It is positive when the line goes up to the right, and negative when the line goes down to the right. It is 0 for a horizontal line.

The slope is found from (x, y) pairs using the formula ...

  m = (y2 -y1)/(x2 -x1) . . . . . . where (x1, y1) and (x2, y2) refer to different pairs

  m = (8 -(-1))/(4 -1) = 9/3 = 3 . . . . using the (x, y) values from the table

The y-intercept (b) is the y-value where the line crosses the y-axis. It can be found by rearranging the slope-intercept equation shown above:

  b = y - mx . . . . . . . for a line with slope m and a point (x, y) on the line

Using the first point listed in the table with the value of m we just found, we see that b is ...

  b = -1 - 3(1) = -4 . . . . . . for (x, y) = (1, -1) and m = 3

Now that we have found m=3 and b=-4 for the points in the table, we can put these values in the slope-intercept equation:

  y = mx +b

  y = 3x -4 . . . . . equation of the relationship in the table

Answer:

7 and 34

Step-by-step explanation:

let x and y be the 2 numbers with x > y

The 2 equations to solve are

x = 4y + 6 → (1)

x + y = 41 → (2)

Substitute x = 4y + 6 into (2)

4y + 6 + y = 41 , that is

5y + 6 = 41 ( subtract 6 from both sides )

5y = 35 ( divide both sides by 5 )

y = 7

Substitute y = 7 into (1)

x = 4(7) + 6 = 28 + 6 = 34

The 2 numbers are 7 and 34

we are given a ring homomorphism f: R → R' between commutative rings R and R'. We need to show that if P is a prime ideal of R' and f^(-1)(P) ≠ R, then the ideal f^(-1)(P) is a prime ideal of R.

To prove this, we first note that f^(-1)(P) is an ideal of R since it is the preimage of an ideal under a ring homomorphism. We need to show two properties of this ideal: (1) it is non-empty, and (2) it is closed under multiplication.

Since f^(-1)(P) ≠ R, there exists an element a in R such that f(a) is not in P. This means that a is in f^(-1)(P), satisfying the non-empty property.

Now, let x and y be elements in R such that their product xy is in f^(-1)(P). We want to show that at least one of x or y is in f^(-1)(P). Since xy is in f^(-1)(P), we have f(xy) = f(x)f(y) in P. Since P is a prime ideal, this implies that either f(x) or f(y) is in P.

Without loss of generality, assume f(x) is in P. Then, x is in f^(-1)(P), satisfying the closure under multiplication property.

Hence, we have shown that f^(-1)(P) is a prime ideal of R, as desired.

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The value of the fourth quartile q3=66.951  when the mean is 63.6 inches and the standard deviation is 2.5 inches.

The normal distribution: This is the distribution of type of continuous probability distribution in which most data points cluster toward the middle of the range, while the rest taper off symmetrically toward either extreme.

The middle of the range is also known as the mean of the distribution.

The mean and standard deviation are given

sd=2.5

μ=63.6

P(X<Q3)=0.75

By using the Z- table we get the value of the inv norm(0.75)

inv norm(0.75)=0.6745

Now know all values to find the Q3 substitute in the Q3 formula

Q3=65.4+23*(0.6745)

   =66..981350

Q3=66.951

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