Your grandfather tells you that he has four coins in his pocket. He has no pennies, and no coin is worth more than a quarter. Calculate all the possible amounts. If Grandpa offers to give you the coins if you are able to guess the amount within ten cents, what is your guess ? Include all combinations in your answer, but include each combination only once be sure to indicate what your guess is.

The measure of angle ADC in the geometric system is equal to 55°.

In this question we find a geometric system formed by a quadrilateral and an angle vertical to a vertex of the quadrilateral. Angle CDE is supplementary to angles EDF and ADC. Two angles are supplementary whose sum of measures equals 180°. Therefore:

m ∠ CDE + m ∠ EDF = 180°

(2 · x + 1) + (x - 7) = 180°

3 · x - 6 = 180°

3 · x = 186°

x = 62

m ∠ CDE = 2 · x + 1

m ∠ CDE = 2 · 62 + 1

m ∠ CDE = 125°

m ∠ ADC = 180° - 125°

m ∠ ADC = 55°

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Answer:

2.5

Step-by-step explanation:

We Know

You buy 4 5/8 blue fabric and 2 1/8 green fabric .

4 5/8 = 37/8 = 4.625 blue fabric

2 1/8 = 17/8 = 2.125 green fabric

How much blue than green did you buy?

We Take

4.625 - 2.125 = 2.5

So, you buy 2.5 blue more than green.

Answer:

Let s = number of single-dip cones

d = number of double-dip cones.

s + d = 60

2.50s + 4.15d = 179.70

2.50s + 4.15(60 - s) = 179.70

2.50s + 249 - 4.15s = 179.70

1.65s = 69.30

s = 42, d = 18

42 single-dip cones, 18 double-dip cones

Answer:

D

Step-by-step explanation:

\(-5+2(7b+6)\geq 10b+7(1+11b)\\-5+14b+12\geq 10b+7+77b\\70b\leq 0\\b\leq 0\)

The equation that represent the gross pay is y = 0.12x + 1760. The commission was $10896 and gross pay was $12656

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Let y represent the gross pay for x total sales.

Donald Simmons a $1760 monthly salary plus a 12% commission on merchandise he sells each month, hence:

y = 1760 + 12% of x

y = 0.12x + 1760

Donald's sales were $90,800 for last month. Hence:

a) Commission = 0.12 * $90800 = $10896

b) Gross pay:

y = 10896 + 1760 = $12656

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Answer: C

Step-by-step explanation:

Use the graph ln the left side.

The description of the graph of the function \(y = \frac{1}{x + 2} + 1\) is the description (c)

The equation is given as:

y = StartFraction 1 Over x + 2 EndFraction + 1?

Rewrite properly as:

\(y = \frac{1}{x + 2} + 1\)

The above equation is the translated equation from an inverse function

The graph of the function pass through the points (0,1.5) and (-3,0)

Hence, the graph of f(x) = √x is (c) On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = -2. One curve opens up and to the right in quadrants 1 and 2. It crosses the y-axis at (0, 1.5). The other curve opens down and to the left, and it crosses the x-axis at (-3, 0).

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Answer:

1:72

Step-by-step explanation:

The scale of a drawing is the ratio of the length in the drawing to the real length.

Drawing length: 7 inches

Real length: 42 ft × 12 in. / ft = 504 in.

Scale:

7 in. to 504 in.

Divide both numbers by 7:

1 in. to 72 in.

Scale: 1:72

Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.

Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.

How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.

Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.

The weight per carton is 55 pounds.

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Answer: See explanation

Step-by-step explanation:

a. Predict the sales resulting from a $15,000 investment in inventory and an advertising budget of $10,000.

To solve this, in the regression equation, we have to replace x1 with 15 and then replace x2 with 10. This will be:

y = 25 + 10x1 + 8x2.

y = 25 + 10(15) + 8(10)

y = 25 + 150 + 80

y = 255

Therefore, the predicted sales is 255.

b. Interpret b1 and b2 in this estimated regression equation.

A change in b1 which is the inventory investment will bring about a change of 10 units in the sales as long as other values are constant.

A change in b2 which is the Advertising expenditure will bring about a change of 8 units in the sales as long as other values are constant.

The number of grams of cocoa is 50.9 grams

This is the mass of an object

Since we have that a chocolate bar contains 53% cocoa and the weight of the chocolate bar is 96 grams.

Let

So, we have that

x = pW

Given that

Substituting the values of the variables into the equation, we have that

x = pW

x = 0.53 × 96 grams

x = 50.88

x ≅ 50.9 grams

So, the number of grams of cocoa is 50.9 grams

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he need 26 centimeters

Answer:

y=-2x+29

Step-by-step explanation:

y-y1=m(x-x1)

y-5=-2(x-12)

y=-2x+24+5

y=-2x+29

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

The value of average temperature during that period=\(58^{\circ}\)

Step-by-step explanation:

We are given that

Temperature at time t  is given by

\(T(t)=50+6t-\frac{1}{3}t^2\)

We have to find the average temperature during a certain  24-hour period.

We know that

Average value of function

\(f_{av}=\frac{1}{b-a}\int_{a}^{b}f(x)dx\)

Using the formula

Average temperature during the period

\(=\frac{1}{24-0}\int_{0}^{24}(50+6t-\frac{1}{3}t^2)dt\)

\(=\frac{1}{24}[50t+3t^2-\frac{1}{9}t^3]^{24}_{0}\)

\(=\frac{1}{24}(50\times 24+3(24)^2-\frac{1}{9}(24)^3)\)

\(=58^{\circ}\)

Hence, the value of average temperature during that period=\(58^{\circ}\)

Answer:

65/100 that is the answer to this question

About 80 necklaces have more than 28 beads. Then the correct option is C.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and the standard deviation is 4 beads.

P(x > 28) = P(x - 24 / 4 > 28 - 24 / 4)

P(x > 28) = P(x - 24 / 4 > 1)

P(x > 28) = 1 - ∅1

P(x > 28) = 1 - 0.8413

P(x > 28) = 0.1587

Multiply both sides by 500, then we have

500 P(x > 28) = 0.1587 × 500

500 P(x > 28) = 79.35

500 P(x > 28) ≈ 80

About 80 necklaces have more than 28 beads. Then the correct option is C.

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The missing options are given below.

A. About 24 devices have more than 28 beads.

B. About 48 necklaces have more than 28 beads.

C. About 80 necklaces have more than 28 beads.

D. About 96 necklaces have more than 28 beads.

The interval that represents the middle 95% of his commute times is [45 , 55]

What is standard deviation ?

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

The empirical rule states that the 95% of the sampled observations will fall within two standard deviations of the mean for a normally distributed population.

Where:

68% is the first standard deviation

95% is the second standard deviation about the mean

99.7% is the 3rd standard deviation about the mean.

Therefore. the middle 95% interval is calculated as:

CI = µ + 2 σ

   =  50 ± 2 (2.5)

   = 50 ± 5

  = [45 , 55]

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Answer:

Triangle RST rises 4 units and runs 8 units.

Triangle XYZ rises 3 units and runs 6 units.

The slope of line b is 1/2.

Step-by-step explanation:

Triangle RST rises 4 units and runs 8 units.

Triangle XYZ rises 3 units and runs 6 units.

The slope of line b is 1/2.

(2, 0) and (8, 3)

m = 3-0/8-2

m = 3/6

m = 1/2

The equation of the line in slope-intercept form is y = 3x + 4.

We can use the combination formula to determine how many different packages can be created from a set of 24 crayons with 36 different colours.

The formula for the mixture is provided by:

n C r equals n!/r! (n-r)!

where r is the number of items we want to choose, n is the total number of items, and! stands for the factorial of a number, which is the sum of all positive integers up to that number.

In this instance, we are trying to determine how many various methods there are to choose 24 crayons from a set of 36 colours, regardless of the sequence in which they are chosen. Consequently, we can apply the following combination formula:

36 C 24 = 36! / (24! * 12!)

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The exponential decay model that represents the forest cover in the world t years after 1990 is:

We can use the exponential decay model to represent the decrease in the world forest cover over time:

y = a e^(kt)

where

y is the forest cover in 10^6 hectares,

t is the time ,

a is the initial forest cover,

k is the decay rate.

Solving for a and k:

where a = 4168 million hectares  (given)

When t = 20  the forest cover was 4033 million hectares.

y = a e^(kt)

y = 4033 = 4168 e^(k*20)

4033/4168 = e^(k*20)

Taking the natural logarithm of both sides:

ln(4033/4168) = k*20

Solving for k, results to

k = ln (4033 / 4168) / 20

k = -0.00165 (to 5 dp)

therefore we can say that, the decay model is:

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Answer:

9:12

Step-by-step explanation:

Answer:

the answer is Less than "<"

Step-by-step explanation:

when you reduce both ratios you get 6:9=2:3 and 9:12=3:4

2:3<3:4

Solution

For this case we can do the following:

And we can create the following two questions:

If we subtract the last two equations we got:

Solving for y^2 we got:

Replacing we got in the first equation:

And solving for x we got:

Answer:

Hello,

Step-by-step explanation:

a)

\(x^2-2x-6=x^2-2x+1-1-6\\\\=(x-1)^2-7\\\)

b)

\(x^2-2x-6=(x-1)^2-7\\\\=(x-1-\sqrt{7} )(x-1+\sqrt{7} )\\\\\\\boxed{x=1-\sqrt{7} \ or\ x=1+\sqrt{7} }\\\)

The direction cosines and direction angles of the vectors will be x/r , y/r , z/r  and cos⁻¹(x/r), cos⁻¹(y/r),cos⁻¹(z/r ) respectively.

The cosines of the angles that a given vector, m = xi + yj + zk, makes well with the x, y, and z axes are the direction cosines of that vector.

If a forms the direction angles (which are cosines) with the x, y, and z axes, then the direction cosines of m are cos a, cos b, and cos c in the x, y, and z axes, respectively.

Let the equation be =  xi + yj + zk

vector of the equation will be = (x, y, z)

r = length of vector = √(x²+y²+z²)

The direction cosines will be x/r , y/r , z/r

angles will be cos⁻¹(x/r), cos⁻¹(y/r),cos⁻¹(z/r )

Direction cosines will be -x/r , y/r , z/r

Angles will be -

cos⁻¹(x/r), cos⁻¹(y/r),cos⁻¹(z/r )

Consider the dimensional point P. We can derive direction cosines by computing the cosine of any positive (anticlockwise) angles that a position vector makes with the positive x, y, and z-axes, respectively.

These angles are referred to as direction angles. By using direction cosines, it is easy to translate a vector's direction into angles with regard to a reference.

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Answer: 570 cm

Step-by-step explanation: The problem is asking 4560 divided by 8, since they are asking the equal distance each player ran. So 4560 divided by 8 is  570 cm.

The distance each player ran for is 570 cm.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.

Given that, a baseball team ran with total distance of 4560 cm, there are 8 players on his baseball team, and they all ran the same number of laps,

We are asked to find the distance each player ran,

The same will be calculated by dividing total distance by total number of players.

Therefore, the distance each player ran = 4560 / 8

= 570 cm

Hence, the distance each player ran for is 570 cm.

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9514 1404 393

Answer:

Step-by-step explanation:

If we assume the ball was kicked from the origin and that it follows a parabolic curve, the equation can be written ...

  y = -kx(x -20)

for some value of k that makes the maximum be 6. The maximum will occur at the value of x that is halfway between the points where the ball is on the ground, so at x=10. Then our value of k is such that ...

  6 = k(10)(20 -10) = 100k

  k = 6/100 = 0.06

The equation describing the ball's flight is ...

  y = 0.06x(20 -x)

A graph is attached.

__

The translated square root function will have a vertical multiplier k that will make it pass through the given point. The parent function f(x) = √x can be translated so its vertex moves from (0, 0) to (-5, 4) by ...

  g(x) = 4 +f(x+5)

Applying the scale factor k gives ...

  g(x) = k·√(x +5) +4

We want g(20) = 29, so ...

  29 = k·√(20 +5) +4

  25 = 5k . . . . subtract 4

  5 = k . . . . . . divide by 5

The equation of the function is ...

  y = 5√(x +5) +4

__

We assume your "graphing form" is "vertex form", as that form is generally conducive to graphing.

We can complete the square by adding and subtracting the square of half the x-coefficient:

  y = x^2 -18x +9^2 +5 -9^2

  y = (x -9)^2 -76 . . . . . equation

  vertex: (9, -76)

  x-intercepts: 9±√76 ≈ {0.2822, 17.1778}

  y-intercept: 5 . . . . (the constant in the given equation)

_____

Additional comment

When the quadratic is written in vertex form ...

  y = a(x -h)^2 +k

the x-intercepts are h±√(-k/a).

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\impliedby y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{3}{5}}x-8\)

so we're really looking for the line of a slope of 3/5 and passing through (0,-3)

\((\stackrel{x_1}{0}~,~\stackrel{y_1}{-3})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{\cfrac{3}{5}}(x-\stackrel{x_1}{0}) \\\\\\ y+3=\cfrac{3}{5}x\implies y=\cfrac{3}{5}x-3\)

The function is defined as g(x) = f (√3x² + 4 ), where "f" is an unknown function.

A function is a mathematical object that assigns a unique output or value for each input. In other words, given an input, a function produces exactly one output.

To understand this function and its properties, we need to first identify and verify the domain and range of the function. The domain of a function is the set of all possible inputs for which the function produces a real output. In this case, the domain of "m" is the set of all real numbers "x" such that the expression √3x² + 4 is real.

Next, we need to understand the composition of functions. In this case, "m" is defined as the composition of two functions, "g" and "f."

The composition of two functions "f" and "g" is defined as "f(g(x))," which means that the output of "g" is used as the input for "f." In other words, we first evaluate "g" for a given value of "x," and then use the output of "g" as the input for "f."

Finally, we can evaluate the function "m" for a specific value of "x" by first evaluating "g" and then "f."

To do this, we simply substitute the value of "x" into the expression for "g" and then evaluate "f" with the resulting output.

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Answer:

108

Step-by-step explanation:

3²(2³+4) calculate to the power of 2 and get 9.

9 (2³+4) calculate 2 to the power of 3 and get 8.

9 (8+4) add 8 and 4 to get 12.

9 · 12 = 108 multiply 9 and 12 to get 108.