Mamá compra una caja de cubitos de azúcar. María se come la capa superior (S), que tiene 77 cubitos; después se come la cara lateral (L), que consta de 55 cubitos; y finalmente se come la cara frontal (F) también. ¿Cuántos cubitos quedan en la caja

Step-by-step explanation:

deca means ten.

a decagon has 10 sides and vertexes.

since the distance from the center to every vertex is equal (4 ft), this means it is a regular decagon (all sides are equal, and also all internal angles are the same).

the described scenario splits the tabletop virtually into 10 congruent isoceles triangles (the legs have the same length : 4 ft, and their 2 baseline angles have the same size). the sides of the decagon are the baselines of these triangles.

we know the inner angles at the top of each triangle, because they are 1/10 of the full circle around the table :

360 / 10 = 36°.

just by remembering that the sum of all angles in a triangle is always 180°, we know also the 2 baseline angles :

180 = 36 + 2×angle

2×angle = 144

each baseline angle is 144/2 = 72°

the area of a triangle is

baseline × height / 2

we can find these 2 lengths by using trigonometric functions of the known angles, and Pythagoras.

the height to the baseline of an isoceles triangle splits the baseline into 2 halves.

so, we have a right-angled triangle with 4 ft being the Hypotenuse, the height and half of the baseline being the legs.

and the angle at the top (center of the table) is 36/2 = 18°.

the third angle is still 72°.

half of the baseline is sin(18)×4 ft.

the height is cos(18)×4 ft

so, the area of one of these isoceles triangles is

2×sin(18)×4 × cos(18)×4 / 2 = sin(18)×cos(18)×16 =

= 4.702282018... ft²

the area of the whole tabletop is then the sum of all 10 triangles :

10×4.702282018... = 47.02282018... ft² ≈ 47 ft²

Step-by-step explanation:

Accumulated value = $20,000.

A = P + I, P = principal, I = Interest.

I = 200*5*t/100

I = 1000t/100 = 10t

2000 = P + I = 200 + 10t

2000 - 200 = 10t

1800 = 10t, t = 180.

Therefore, it would take her 180 years to save $20,000.

Step-by-step explanation:

36/6 or it is just 6 depends on if you need it as a fraction or not

Answer:

8 sec^2 x + 4 tan^2 x − 12 = 0     →     sec^2x = tan^2x + 1

8 [ tan^2x + 1] + 4tan^2x - 12  = 0

8tan^2x + 8 + 4tan^2x - 12  = 0

12tan^2x - 4   = 0     divide through by 4

3tan^2x - 1  = 0

3tan^2x  =  1  

tan^2x  = 1/3      take the square root of both sides

tanx = ±1 / √

Answer:

If the base and the negative exponent is in the denominator already

Step-by-step explanation:

Normally, a base with a negative exponent moves to the denominator.

Example: (2^-3 = 1 / (2)^3 = 1/8)

However, if the base and the negative exponent is already in the denominator, the base would move to the numerator and the exponent would become positive.

Example:  2 / (3)^-3 = 2 * 3^3 = 2 * 27 = 54

Answer:

C. HA

D. AAS

Step-by-step explanation:

∆HIJ is a right triangle with a given labelled acute angle and a given hypotenuse, which are congruent to the acute angle and hypotenuse length of ∆KLM, by on the Hypotenuse-Acute Angle Theorem (HA), ∆HIJ and ∆KLM are congruent.

Also, the two triangles have two given angles that are congruent, and a non-included side (hypotenuse), which are congruent in both triangles, by definition of the AAS congruency theorem, both triangles can be said to be congruent.

Therefore, the congruency theorems that could be given as reasons why both triangles are congruent to each other are the HA and AAS theorems.

Answer:

The correct answer is HA and AAS.

Step-by-step explanation:

The HA (hypotenuse angle) states "if the hypotenuse and one acute angle of a right triangle are congruent to the hypotenuse an done acute angle of another triangle, then the triangles are congruent.

The AAS (angle-angle-side) theorem states "If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of a second triangle, then the triangles are congruent.

It would take 370 days to build the wall with the given conditions.

If 60 men can build a wall in 40 days, then the total man-days required to build the wall is:

60 men x 40 days = 2400 man-days

However, 55 men quit every ten days, which means that after 10 days, there are only 60 - 55 = 5 men left to work on the wall. After 20 days, there are only 5 - 55 = -50 men left, which means that the remaining 5 men cannot work any faster than they were already working. Therefore, we can assume that the remaining 5 men complete the wall on their own.

The number of man-days required for the first 10 days is:

60 men x 10 days = 600 man-days

The number of man-days required for the second 10 days is:

5 men x 10 days = 50 man-days

The total number of man-days required for the first 20 days is:

600 man-days + 50 man-days = 650 man-days

The remaining work can be completed by the 5 men in:

2400 man-days - 650 man-days = 1750 man-days

Therefore, the total time needed to build the wall is:

20 days + 1750 man-days / 5 men = 20 + 350 days = 370 days

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Answer:

1/2=10

Step-by-step explanation:

it depends upon the area of the triwngle

The Slope Intercept Form is y = -11

What is Slope?

The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line. The letter m is frequently used to represent slope; there is no obvious answer to why the letter m is chosen for slope.

Solution:

Given:

(x1 , y1) = (-5, -11) and

(x2, y2) = (3, -11)

Slope = y2 -y1 / x2 - x1 = -11+11 / 3+5

Slope = 0

Point Slope Form:

y - y1 = m (x - x1)

y + 11 = 0

Slope Inetrcept Form:

y = mx + b

y = 0 - 11

y = -11

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Answer:

3:5

Step-by-step explanation:

To find the simplest ratio, divide each number by 2:

6/2

= 3

10/2

= 5

So, the simplest ratio of triangles to squares is 3:5

Answer:

2x-y=4

Step-by-step explanation:

Standard form of a line: Ax+by=c

Use slope intercept form: y=mx+b

slope= 2

y=2x-4

Add 4 to both sides.

y+4=2x

subtract y from both sides.

4=2x-y

Rotate the equation

2x-y=4

Answer:

2x-y=4

Step-by-step explanation:

y=2x-4 is the slope intercept.

y-2x=-4

-2x+y=-4

2x-y=4

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{11}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{RT} \end{cases} \\\\\\ RT=\sqrt{ 11^2 - 6^2}\implies RT=\sqrt{ 121 - 36 } \implies RT=\sqrt{ 85 }\implies RT\approx 9.22\)

Answer: 100

Step-by-step explanation: 50 x 1/2=100

The equation that can be used to find the cost of each binder n in dollars is 861=7n.

Given that the cost of 7 binders is $8.61.

We are required to form an equation that represents the total cost of each binder n in dollars.

Equation is like a relationship between all the variables that are expressed in equal to form.It may be linear equation or may be more types.

Suppose the cost of 1 binder is n dollar.

We know that the total cost is basically the product of price of 1 unit and number of quantities of units.

Total cost=Price of 1 unit* number of units

8.61=n*7

8.61=7n

Hence the equation that can be used to find the cost of each binder n in dollars is 861=7n.

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here's your answer..

Answer:

1km

Step-by-step explanation:

1000m=1km

Ez Money

Answer:

1000m= 1km

if you convert 1m to km is 0.001km times it by 1000, you get 1km.

Answer:  One-third the sum of negative fifty-four and fifteen is -15.

Step-by-step explanation:

Answer:

A chip of 16.59 ounces represents the 67th percentile for the bag weight distribution

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 16.5, \sigma = 0.2\)

What chip amount represents the 67th percentile for the bag weight distribution

This is X when Z has a pvalue of 0.67, so X when Z = 0.44.

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

\(0.44 = \frac{X - 16.5}{0.2}\)

\(X - 16.5 = 0.44*0.2\)

\(X = 16.59\)

A chip of 16.59 ounces represents the 67th percentile for the bag weight distribution

Using the normal distribution concept, the chip amount which corresponds to the 67th percentile is 16.59

Using the concept of normal distribution :

The 67th percentile is defined as :

P(Z < 0.67) ; Using a normal distribution table, the corresponding Zscore value is 0.44

Substitute into the Zscore relation and solve for the score, X :

0.44 = (X - 16.5) / 0.2

Cross multiply

0.44 × 0.2 = (X - 16.5)

0.088 = X - 16.5

0.088 + 16.5 = X

X = 16.588

Therefore, the chip amount is 16.59.

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Answer:10907

Step-by-step explanation 10907

Answer:

The answer is 28

Step-by-step explanation:

Hope this helps,

have a great day

Answer:

78/2=39°

Step-by-step explanation:

thx for the points

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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To obtain how much money the customer left for the tip, we need to find 18% of $34.

For this, we need to multiply 34 by 18, and then divide the result by 100. Therefore:

Then, the customer left $6.12 for the tip.

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

A. To represent the number of grams present after n hours, we can use the equation:

N(n) = 15 × (1 - 0.2)^n

Where:

N(n) is the number of grams present after n hours,

15 is the initial amount of the substance in grams,

0.2 represents the decay rate of 20% per hour, and

^n represents the exponentiation operation.

B. To find out how much will be left after 24 hours, we can substitute n = 24 into the equation from part A:

N(24) = 15 × (1 - 0.2)^24

Calculating this expression, we find that approximately 2.49 grams will be left after 24 hours.

C. We need to determine the number of hours it takes until there is approximately one gram left. We can set up the equation:

1 = 15 × (1 - 0.2)^n

To solve for n, we can divide both sides of the equation by 15 and then take the logarithm (base 0.8) of both sides:

log(0.8)(1/15) = n

Using a calculator or logarithmic properties, we find that approximately 18.13 hours are required until there is approximately one gram left.

Therefore, the answers are:

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

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The fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

A fraction is a numerical representation of the division of the two terms x and y, as follows:

Fraction = x/y.

As the rate is PKR 1 = 50 paisas, we have that the fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

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The value of x is 1.75 and y is 5. The solution is obtained using properties of congruent triangles.

What is a congruent triangle?

Two triangles that are congruent will have precisely the same three sides and three angles.

The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions.

The triangles are congruent by SAS congruency because

AC = CD (Given)

∠ACB = ∠DCE ( Vertically opposite angles)

BC = CE  (Given)

Thus, Triangle ABC ≅ Triangle DEC

Since, the triangles are congruent, therefore

⇒AC = CD

⇒4y-6 = 2x+6   ...(1)

Also, BC = CE

⇒3y+1 = 4x

⇒(3y+1)/4 = x    ...(2)

Now, substituting the value of x in (1), we get,

⇒4y-6 = 2(3y+1)/4+(6)

⇒4y-6 = (6y+2 +24)/4

⇒16y-24 = 6y+2 +24

⇒10y = 50

⇒y = 5

Now putting the value of y in (2), we get

⇒(3(2)+1)/4 = x

⇒7/4 = x

⇒ x = 1.75

Hence, the value of x is 1.75 and y is 5.

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Answer:

The square root of 50 is approximately 7.07.

Answer:

7.07106781187...

Step-by-step explanation:

its an irrational number

Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.

To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.

First, let's isolate the absolute value term on one side of the equation:

|3x + 3| = -3

Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.

To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:

   3x + 3 = -3

   -(3x + 3) = -3

Solving equation 1:

3x + 3 = -3

3x = -6

x = -2

Solving equation 2:

-(3x + 3) = -3

-3x - 3 = -3

-3x = 0

x = 0

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Answer:

A. or every 1 ton increase in precompression stress, the shear strength of the joint is estimated to increase by 0.987 tons.

Step-by-step explanation:

Hello!

The engineers created a regression model to estimate the relationship between the "shear strength of masonry joints" (Y), measured in tons, and the "precompression stress" (X), measured in tons.

^Y= a + bXi

Using the regression output:

Estimate of the y-intercept: a= 1.192

Estimate of the slope: b= 0.987

In general terms you can interpret the slope as:

"Is the modification of the estimated mean of Y when X increases one unit"

In this case it means that every time the precompression stress increases one ton, the shear strength of the joint is estimated to increase 0.987 tons.

I hope this helps!

Answer:

5

Step-by-step explanation:

Use the Exterior Angle Theorem.

The E.A.T states that the measurement of an exterior angle is found by adding the two opposite and non-adjacent interior angles.

In this case, the Exterior Angle is 121. The sum can be found by combining 17x - 4 and 8x. Set the equation:

17x - 4 + 8x = 121

First, combine like terms:

17x + 8x - 4 = 121

(17x + 8x) - 4 = 121

(25x) - 4 = 121

Next, Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, add 4 to both sides of the equation:

25x - 4 (+4) = 121 (+4)

25x = 121 + 4

25x = 125

Next, divide 25 from both sides:

(25x)/25 = (125)/25

x = 125/25

x = 5

5 is your value for x.

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