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Evaluate 7⋅5+42−23÷4 '

49 41 34 9

Answer:

drippy pen iss

Step-by-step explanation:

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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In the given case, each loaf of bread contains 25/18 cups of flour.

To find how many cups of flour are in each loaf of bread, we need to divide the total amount of flour by the number of loaves.

First, let's convert the mixed numbers to improper fractions:

\(2 2/3 cups = 8/3 cups\)

\(1 1/2 cups = 3/2 cups\)

Next, we can add the two fractions to find the total amount of flour:

8/3 cups + 3/2 cups = (16/6 + 9/6) cups = 25/6 cups

So, the recipe requires 25/6 cups of flour to make 3 loaves of bread.

To find the amount of flour in each loaf, we divide 25/6 cups by 3:

(25/6 cups) / 3 = 25/18 cups

Therefore, each loaf of bread contains 25/18 cups of flour.

Alternatively, we could simplify the mixed numbers at the beginning:

2 2/3 cups = 8/3 cups

1 1/2 cups = 6/4 cups

Then we can add the fractions:

8/3 cups + 6/4 cups = (32/12 + 18/12) cups = 50/12 cups

Finally, we can divide by 3 to find the amount of flour in each loaf:

(50/12 cups) / 3 = 25/18 cups

So the answer is the same.

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When applying the some rule, we only combine two equal ratios at once. Consequently, we deal with pairs of sides and angles that have equivalent ratios.

When two ratios are equal, a percentage is formed; alternatively, two equal ratios can be said to produce a proportion. When we understand that two ratios are equal, you can write a proportion. The ratios of these two numbers are equal.

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant. Two angles are said to be complimentary if their sum is 90 degrees. Alternatively put, two angles are said to be complimentary if they combine to make a right angle.

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Answer:

57,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

y - 3 = -2/3(x - 3)

y - 3 = -2/3x + 2

y = -2/3x + 5

Answer:

The answer is 275 students.

Step-by-step explanation:

In 75 students, 33 students attend.

So the ratio is 33/75.

so multiply with 625.

625 x 33/75 = 275

Answer:

4.326 x 10^ 3

Step-by-step explanation:

Correct me if wrong please :)

Area of semicircle is 77.

What is semicircle?

A semicircle is defined as half circle formed by cutting the circle into two halves.

Given that;

Diameter of semicircle = 14

Radius of semicircle = 14/2 = 7

Now, Area of semicircle = 1/2 (πr²)

Substitute π = 22/7 and r = 7, we get;

Area of semicircle = 1/2 (πr²)

                             = 1/2 × (22/7) × 7 × 7

                             = 77

So, Area of semicircle is 77.

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To write the given equation in logarithmic form, we can use the definition of logarithms. The equation 10^m = w can be rewritten as a logarithm with base 10: log10(w) = m

The general relationship between exponents and logarithms is as follows:

base^(exponent) = result

In logarithmic form, it's written as:

log_base(result) = exponent

For our given equation, 10^m = w, we have:

base = 10

exponent = m

result = w

Applying the general logarithmic relationship, we write:

log10(w) = m

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Answer:

a) 0.0537 = 5.37% probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes

b) 0.9871 = 98.71% probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mildly obese:

Mean 376 minutes and standard deviation 67 minutes, which means that \(\mu = 376, \sigma = 67\)

Sample of 6

This means that \(n = 6, s = \frac{67}{\sqrt{6}} = 27.35\)

Lean

Mean 520 minutes and standard deviation 110 minutes, which means that \(\mu = 520, \sigma = 110\)

Sample of 6

\(n = 6, s = \frac{110}{\sqrt{6}} = 44.91\)

A) What is the probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes?

This is 1 subtracted by the pvalue of Z when X = 420, using the mean and standard deviation for mildly obese people. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{420 - 376}{27.35}\)

\(Z = 1.61\)

\(Z = 1.61\) has a pvalue of 0.9463

1 - 0.9463 = 0.0537

0.0537 = 5.37% probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes.

B) What is the probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes?

This is 1 subtracted by the pvalue of Z when X = 420, using the mean and standard deviation for lean people. So

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{420 - 520}{44.91}\)

\(Z = -2.23\)

\(Z = -2.23\) has a pvalue of 0.0129

1 - 0.0129 = 0.9871

0.9871 = 98.71% probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes

Answer:

12

Step-by-step explanation:

3+2+7=12

Hope this helps! Please give brainliest!

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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E

Step-by-step explanation:

volume of big shape + volume of small shape

(9+6×5)+(6×3×2)

=306

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

\(x = 7\)

Step-by-step explanation:

Given

The attached figure

Required

Find x

Since both shapes are similar, then:

\(LM : KN = RV : SP\)

This gives:

\(4x + 4 : 7x - 9 = 48 : 60\)

As fraction:

\(\frac{4x + 4 }{ 7x - 9} = \frac{48 }{ 60}\)

Simplify:

\(\frac{4x + 4 }{ 7x - 9} = \frac{4 }{ 5}\)

Cross Multiply:

\(5(4x + 4) = 4(7x - 9)\)

\(20x + 20 = 28x - 36\)

Collect Like Terms

\(28x - 20x = 20 + 36\)

\(8x = 56\)

\(x = 7\)

Answer:

Step-by-step explanation:

Given

\(x=1-sin(a)\\y=1+cos(a)\)

Solve for \(a\) in the second equation.

\(y=1+cos(a)\)

\(y-1=cos(a)\)

\(a=cos^{-1}( y-1)\)

Insert our answer for \(a\) into the first equation.

\(x=1-sin(a)\)

\(x=1-sin(cos^{-1}( y-1))\)

\(cos^{-1}=arccos\)

\(x=1-sin(arccos( y-1))\)

Lets simplify \(1-sin(arccos( y-1))\)

A piece of graph paper would be helpful in my opinion.

Here is how I would go about doing so

Draw a triangle in the plane with vertices \((y-1,\sqrt{1^2-(y-1)^2}),(y-1,0)\) and the origin.

\(arccos(y-1)\) is is the angle between the positive x-axis and the ray beginning at the origin and passing through \((y-1,\sqrt{1^2-(y-1)^2})\). Therefore \(sin(arccos(y-1))\) is \(\sqrt{1-(y-1)^2}\)

Now we have

\(x-1-\sqrt{1-(y-1)^2}\\a=arccos(y-1)\)

We can write \(1\) as \(1^2\). Since both terms are now perfect squares, we can factor using the difference of squares formula.

\(a^2-b^2=(a+b)(a-b)\) where \(a=1\) and \(b=y-1\)

\(x=1-\sqrt{(1+y-1)(1-(y-1))}\)

After simplifying we get

\(x=-\sqrt{y(-y+2)}+1\)

\(x=-\sqrt{y(-y+2)}+1\)

\(a=arccos(y-1)\)

I think this is what your question was. If not let me know.

Step-by-step explanation:

To calculate the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity, we can use the formula for the present value of an annuity due:

PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)

where:

- PV is the present value of the annuity due ($32,000)

- PMT is the monthly payment we want to find

- r is the annual interest rate (7.9%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PMT = PV / ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n) = **$292.07**

Therefore, the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity is **$292.07**.

P11 equals  769.417 and general formula is 19*(1.4)^(n)

Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself

The growth rate is .4 per time period.

the exponential growth model is f = p * (1 + .4) ^ n

f is the future value.

p is the present value.

r is the growth rate per time period.

n is the number of time periods.

in p0, n = 0

in p11, n = 11

you are given that p0 = 19

in the formula, that becomes f = 19 * (1 + .4) ^ 0 = 19 * (1.4) ^ 0 = 19.

the formula for p1 becomes f = 19 * (1 + .4) ^ 1 = 19 * (1.4) ^ 1 = 26.6

the formula for p11 becomes f = 19 * (1 + .4) ^ 11 = 19 * (1.4) ^ 11 = 769.417

the formula for pn becomes = 19*(1.4)^(n)

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The time interval between the first two instants when this element has a position of y = 0. 175 m is 21 ms.

The time interval between the first two instants when this element has a position of y = 0. 175 m is calculated as;

y (x, t) = ( 0.35 m sin[1.25 rad/m)x  + (99.6 rad/s)t]

x = 0

y(0,t) =  0.35 sin(1.25 rad/m)0 + 99.6t ) = 0.175

0.35 sin(99.6t) = 0.175

sin (99.6t) = 0.175/0.35

sin (99.6t) = 0.5

99.6t = sin⁻¹ (0.5)

99.6t = (π/6 ) or ( π - π/6) = 5π/6

time, t₁ = ( π/6 ) / ( 99.6 ) = 5.257 x 10⁻³ s

time, t₂ = ( 5π/6 ) / ( 99.6 ) = 26.28 x 10⁻³ s

time interval = t₂ - t₁

= 26.28 x 10⁻³ s - 5.257 x 10⁻³ s

= 21 x 10⁻³ s

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The complete question is below:

A transverse wave on a string is described by the equation

y (x, t) = ( 0.35 m) sin[1.25 rad/m)x  + (99.6 rad/s)t]

Consider the element of the string at x = 0.

What is the time interval between the first two instants when this element has a position of  y = 0. 175 m?

After the transformation point A will be at (5, 6.586), point B will be at (5.121, 7.121) and point C will be at (6.121, 5.121).

The coordinates of a triangle after rotation and translation can be found using the following steps:

       x' = (x - a) * cos(θ) - (y - b) * sin(θ) + a

       y' = (x - a) * sin(θ) + (y - b) * cos(θ) + b

        x' = x + dx

        y' = y + dy

       x' = (1 - 2) * cos(45) - (3 - 4) * sin(45) + 2 = -1.121 + 1.121 + 2 = 2.000

       y' = (1 - 2) * sin(45) + (3 - 4) * cos(45) + 4 = -0.707 - 0.707 + 4 = 2.586

      x' = 2 + 3 = 5

      y' = 2.586 + 4 = 6.586

     similarly for point B(2,5) will be (5.121,7.121)

     and for point C(3,3) will be (6.121,5.121)

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Answer:

  $442.42

Step-by-step explanation:

You want the remaining available credit on a credit line of $500 when charges of $25.25 and $32.33 have been made.

The remaining credit is the original credit amount less the amount of credit used:

  $500 -25.25 -32.33 = $442.42

Cameron has credit of $442.42 available.

The approximate height of the tree is given as follows:

45.6 ft.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

14.5 ft.

The bases are given as follows:

5.2 ft and x ft.

Hence the value of x is given as follows:

5.2x = 14.5²

x = 14.5²/5.2

x = 40.4 ft.

Hence the height of the three is given as follows:

5.2 + 40.4 = 45.6 ft.

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Answer:

cost of paint set = $ 13.64

cost of sketch book = $ 6.82

cost of brush = $ 4.55

Step-by-step explanation:

Let the cost of paint set is s.

cost of sketch book = s/2

cost of brush = s/3

Money spent = $ 28 - $ 3 = $ 25

So,

s +  s/2 + s/3 = 25

6 s + 3 s + 2 s = 150

11 s = 150

s = $ 13.64

cost of paint set = $ 13.64

cost of sketch book = $ 6.82

cost of brush = $ 4.55

Answer:

Square Meters to Square Inches Conversion 1 Square meter is equal to 1550.0031 square inches. To convert square meters to square inches, multiply the square meter value by 1550.0031.

The Least-squares problem that has minimal norm can be given using factorization.

The least squares method is used to find the best fit for a set of data points by minimizing the sum of the offsets from the plotted curve. Singular value decomposition (SVD) is a factorization of a real or complex matrix.

here, we have,

It is a widely used technique to decompose a matrix into several component matrices, exposing many of the useful and interesting properties of the original matrix. The singular value decomposition, guaranteed to exist, is A=UΣV.

When we have the equation system Ax=b, we calculate the SVD of A as A=UΣVT. The matrices U and VT have a very special property. They are unitary matrices. One of the main benefits of having unitary matrices like U and VT is that if we multiply one of these matrices by its transpose (or the other way around), the result equals the identity matrix.

The singular value decomposition (SVD) of matrix A is very useful in the context of least squares problems. It is also very helpful for analyzing the properties of a matrix.

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Complete question:

calculate least squares solution using svd a matrix has the singular value decomposition what is the solution to the least-squares problem that has minimal norm ?

The volume of the composite figure made of a rectangular and triangular prism is 216 in³

Volume of rectangular prism = length * width * height

Given the following parameters:

l = 6in

w = 6in

h = 4in

Substitute

V = 6 * 6 * 4

V = 144in³

The volume of the triangular prism = 1/3(6*4)*6
The volume of the triangular prism = 72 in³

Hence the volume of the figure  = 144in³ + 72 in³
The volume of the figure = 216 in³

Therefore the volume of this figure is 216 in³

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