While visiting a pet store, you notice that there are only birds and cats in the cages. You can't help but wonder how many of each animal there is in the yard. But when you ask the store manager how many of each animal he has, he refuses to give you a direct answer. He says there are 16 animal heads and 42 animal feet. How many birds and cats are there in the pet store?

Answer:

The length of the shadow is increasing with the rate of 1.5 feet per sec

Step-by-step explanation:

Let AB and CD represents the height of the lamppost and child respectively ( shown below )

Also, let E be a point represents the position of child.

In triangles ABE and CDE,

[tex]\angle ABE\cong \angle CDE[/tex]    ( right angles )

[tex]\angle AEB\cong \angle CED[/tex]  ( common angles )

By AA similarity postulate,

[tex]\triangle ABE\sim \triangle CDE[/tex]

∵ Corresponding sides of similar triangles are in same proportion,

[tex]\implies \frac{AB}{CD}=\frac{BE}{DE}[/tex]

We have, AB = 12 ft, CD = 4 ft, BE = BD + DE = 6 + DE,

[tex]\implies \frac{12}{4}=\frac{6+DE}{DE}[/tex]

[tex]12DE = 24 + 4DE[/tex]

[tex]8DE = 24[/tex]

[tex]DE=3[/tex]

Now, the speed of walking = 2 mph = [tex]\frac{2\times 5280}{3600}\approx 2.933\text{ ft per sec}[/tex]

Note: 1 mile = 5280 ft, 1 hour = 3600 sec

Thus, the time taken by child to reach at E  

[tex]= \frac{\text{Walked distance}}{\text{Walking speed}}[/tex]

[tex]=\frac{6}{2.933}[/tex]

= 2.045 hours

Hence, the change rate in the length of shadow

[tex]= \frac{\text{Length of shadow}}{\text{Time taken}}[/tex]

[tex]=\frac{3}{2.045}[/tex]

= 1.5 ft per sec.

The solution is in the attachment

The height of the rose after 10 weeks was approximately 7.714 inches. This is calculated by multiplying the original height of the rose (5.8 inches) by 1 1/3 (converted to a decimal as 1.33).

The subject of this question is Mathematics, and it involves performing multiplication to find the height of the rose after 10 weeks. Given that the height of the rose was 5.8 inches originally, and after 10 weeks, the height was 1 1/3 times the original height, we can calculate the new height as follows:

So, 5.8 inches * 1.33 = 7.714 inches.

Therefore, the height of the rose after 10 weeks was approximately 7.714 inches.

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Answer:

(4,0,-5)

Step-by-step explanation:

Since we move 4 points along +ve x-axis so,  x coordinate is 4

We did not move any point along y-axis so  y coordinate is 0

we moved 5 points along -ve z-axis so z coordinate is -5

so our position is (x,y,z) = (4,0,-5)

Answer:

biases

Step-by-step explanation

i toke the test

Bias is the systematic tendency to use information about others.

The propensity to give facts that can be quickly recalled from memory as much weight as possible while making a decision.

You may reap the rewards of group judgments while avoiding frequent challenges to effective judgment in groups by managing group judgment processes well. Fundamental judgment ideas may be learned, but like with other abilities, practice is required. A professional judgment framework is a useful example of a sound decision-making procedure and enables you to identify potential areas for error. A shared framework enables the use of a common language and understanding. It normally pays off to put in some work up front, especially in the initial few stages of the judging process.

Therefore, A few properties of systematic bias are Heuristics are quite effective; typically speaking, benefits outweigh costs; yet, they may lead to biased judgment.

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Answer:

[tex]CD = 7.8[/tex]

Step-by-step explanation:

Given:

Δ DBC is a right angled triangle.

[tex]\angle B = 90\°\\\\\angle C = 59\°[/tex]

BC = 4

We need to find the value of CD

Solution:

Now we know that:

[tex]cos\ \theta = \frac{adjacent \ side}{hypotenuse}[/tex]

So we can say that;

[tex]Cos \angle C =\frac{BC}{CD}[/tex]

Substituting the given values we get;

[tex]Cos\ 59 = \frac{4}{CD}\\\\\\CD = \frac{4}{Cos\ 59} = 7.766[/tex]

Rounding to nearest tenth we get;

[tex]CD = 7.8[/tex]

Hence the Value of CD is 7.8.

Answer:

The answer to your question is 25 girls

Step-by-step explanation:

Data

4 boys for every 5 girls

20 boys             ? number of girls

To solve this problem use proportions

Number of boys : Number of girls :: New number of boys : New number of

                                                                                                          girls

Substitution

                                       4 : 5 ::  20 : x

Solve for x

                                       x = (5 x 20) / 4

Simplification

                                      x = 100 / 4

Result

                                      x = 25

There are 25 girls                                

Answer: the value of the account at the end of 6 years is is $8577

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 6000

r = 6% = 6/100 = 0.06

n = 4 because it was compounded 4 times in a year.

t = 6 years

Therefore,.

A = 6000(1+0.06/4)^4 × 6

A = 6000(1+0.015)^24

A = 6000(1.015)^24

A = $8577

Answer:

The answer to your question is right

Step-by-step explanation:

Acute is a triangle in which three internal angles are acute (less than 90°). The other angles measure  90°, so this option is incorrect.

Obtuse is a triangle that has one angle greater than 90°. This option is incorrect because of the angles of this triangle measure 30, 60, 90.

Equiangular is a triangle in which angles measures the same. This option is wrong because the angles have different values.

A Right triangle is a triangle that has an angle that measures 90°. This option is right.

9514 1404 393

Answer:

  CD = 8 ft.

  BD = 8 ft.

Step-by-step explanation:

To make use of the SAS postulate, Anna needs to identify two sides on either side of congruent angles.

The only marked angle is the right angle. We know that AD is congruent to itself, so Anna also needs to use the segments CD and BD, which are on the other side of the right angle in the right triangles.

The two choices in which BD and CD have the same length are

Final answer:

The estimated tuition at this college in 2020 is $51,137.

Explanation:

To find the equation to determine the tuition y for x years after 2000, we need to use the given information: the annual tuition in 2000 was $20,500 and it increased to $45,120 in 2018.

Let's calculate the rate of increase per year:

The change in tuition over the number of years is:

(Tuition in 2018 - Tuition in 2000) / (Year in 2018 - Year in 2000) = (45,120 - 20,500) / (2018 - 2000)

Now, we can use this rate of increase to find the tuition in any given year x:

Tuition in a specific year = Tuition in 2000 + (Rate of increase per year) * x

To estimate the tuition in 2020, we substitute x = 20 into the equation:

Tuition in 2020 = 20,500 + ((45,120 - 20,500) / (2018 - 2000)) * 20 = $51,137

Answer:

What am I suppose to do?

Step-by-step explanation:

Answer:

Step-by-step explanation:

(2x+y)(3x²+y)=2x(3x²+y)+y(3x²+y)=6x³+2xy+3x²y+y²=6x³+3x²y+2xy+y²

Answer:

52.814 degrees

Step-by-step explanation:

we know that

[tex]1^o=60'\\1'=60''[/tex]

we have

[tex]52^o48'51''[/tex]

[tex]52^o48'51''=52^o+48'+51''[/tex]

Convert 51'' to minutes

[tex]51''=\frac{51}{60}= 0.85'[/tex]

[tex]52^o48'51''=52^o+48'+0.85'=52^o+48.85'[/tex]

Convert 48.85' to degrees

[tex]48.85'=\frac{48.85}{60}= 0.814^o[/tex]

[tex]52^o+48.85'=52^o+0.814^o=52.814^0[/tex]

Final answer:

The angle measure 52°48'51'' is equivalent to 52.814 degrees in decimal form when you convert the minutes and seconds to a decimal and add them to the degree part.

Explanation:

The angle measure 52°48'51'' equivalent to in decimal degrees is calculated by converting minutes and seconds to a decimal form. One degree equals 60 minutes, and one minute equals 60 seconds. To convert, divide the number of minutes by 60 and the number of seconds by 3600, then add those amounts to the degrees to get the decimal degree.

Starting with the minutes: 48 minutes / 60 = 0.8 degrees.

Now converting the seconds: 51 seconds / 3600 = approx. 0.014167 degrees.

So, adding these together: 52 + 0.8 + 0.014167 = 52.814167 degrees, which rounded to the nearest thousandth of a degree is 52.814.

The total water needed to fill the pool is 75π cubic feet.

Given: The pool is 10 feet in diameter and 3 feet tall. To find: The total water needed to fill the pool using V = πr²h formula.

Calculations: Radius (r) = 5 feet, Height (h) = 3 feet. Substitute values into formula: V = π(5)^2(3) = 75π cubic feet.

Answer: The total water needed to fill the pool is 75π cubic feet.

Answer:

5.28°

Step-by-step explanation:

Draw the triangle formed by the sledding run.  The hypotenuse is 300.  The height is 27.6.  The angle of depression is opposite of the height.

Using sine:

sin θ = 27.6 / 300

sin θ = 0.092

θ = 5.28°

Answer:

[tex] k = - \frac{40 W/m^2}{\frac{20-40 C}{0.05 m}}= 0.1 \frac{W}{m C}[/tex]

Step-by-step explanation:

Previous concepts

The Fourier's law, states that the "rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows".

And we have the following formula given:

[tex] q_x = -k A \frac{dT}{dx}[/tex]

For this case we have the following data given:

[tex] L= 50 mm * \frac{1m}{1000 mm}=0.05m[/tex]

[tex] T_i = 40 C[/tex] represent the inner surface temperature

[tex] T_o = 20 C[/tex] represent the outer surface temperature

[tex] \frac{q_x}{A} = 40 W/m^2 [/tex] represent the heat flux

So then we are interested on the value of k.

Solution to the problem

if we solve for the value of k from the formula:

[tex] q_x = -k A \frac{dT}{dx}[/tex]

We got:

[tex] k = - \frac{q_x}{A \frac{dT}{dx}}[/tex]

We can rewrite this expression like this:

[tex] k = - \frac{q_x}{A \frac{T_o -T_i}{L}}[/tex]

And if we replace the values given we got:

[tex] k = - \frac{40 W/m^2}{\frac{20-40 C}{0.05 m}}= 0.1 \frac{W}{m C}[/tex]

Using Fourier's law of heat conduction, the thermal conductivity of the wood slab is calculated to be 0.1 W/m·K given a heat flux of 40 W/m², a temperature difference of 20°C, and a thickness of 50 mm.

The student is asking about the thermal conductivity of a wood slab, given its thickness, the temperature difference across it, and the heat flux. To find the thermal conductivity (k), we can use Fourier's law of heat conduction which states:

Q/t = k × A × (T2 − T1) / d

where:

Rearranging the formula to solve for k gives:

k = Q/t × d / (T2 − T1)

Plugging in the values:

k = 40 W/m² × 0.05 m / 20°C

k = 0.1 W/m·K

So, the thermal conductivity of the wood is 0.1 W/m·K.

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Answer:

The total area of the rectangle is found by counting the total number of 1 cm squares inside the rectangle.

Note: This question is missing some details.

A more complete question is this: Use a ruler to measure the side lengths of the rectangle in centimeters. Mark each centimeter with a point and connect the points to show the square units. Then, count the squares you drew to find the total area.

Step-by-step explanation:

This method is used to determine area of a rectangle by counting the square unit inside the given rectangle.

For example, if the measurement of the sides of the rectangle is 8 cm and 5 cm respectively. To find the area;

Step 1: Mark out 1 cm points on each side of the rectangle.

Step 2: Connect each of the points.

Step 3: Count the number  1 cm squares within the triangle. The total number of squares gives the area of the triangle.

In this example, the number of 1 cm squares will be found to be 40. So the area of the rectangle is 40 cm squares or 40 cm².

Andre can complete 1.5 facts in one second.

Step-by-step explanation:

Given,

Number of multiplication facts completed in 90 seconds = 135

Therefore;

90 seconds = 135 facts

Dividing both sides by 90 to fins the facts per second

[tex]\frac{90}{90}\ seconds=\frac{135}{90}\ facts\\\\1\ second = 1.5\ facts[/tex]

Andre can complete 1.5 facts in one second.

Keywords: unit rate, division

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Andre can answer 1.5 multiplication facts per second by dividing the total number of facts he completed (135) by the time it took (90 seconds).

Andre has been answering multiplication facts at a consistent pace. To find out how many facts he can answer per second, we need to divide the total number of facts he answered by the total number of seconds it took him to answer them.

Andre answered 135 multiplication facts in 90 seconds.

To calculate the rate per second, the formula is:

Therefore, Andre can answer 1.5 facts per second.

Answer:

Variability expected among these Proportions is given by Standard deviation = 0.125

Step-by-step explanation:

The probability of tossing heads is the same for a fair coin as the probability of tossing tails.

The probability of tossing heads is then 1 chance out of 2

P = 1/2 = 0.5

The standard deviation of the sample distribution of the sample proportion = √Pq/n

Standard deviation = √p(1-p)/n

= √0.5(1-0.5)/16

Standard deviation = 0.125

The variability among the proportions of heads obtained in the coin tosses is due to the random nature of the experiment. The law of large numbers explains that as the number of tosses increases, the observed relative frequencies of heads will approach the theoretical probability of 0.5.

The amount of variability that can be expected among the proportions of heads obtained by the students tossing a coin 16 times can be determined by understanding the concept of probability.

In a single coin toss, the probability of getting a head is 0.5. However, when the coin is tossed more times, the observed proportions of heads will vary from the theoretical probability of 0.5.  

The variability among these proportions is attributed to the random nature of the coin tosses and is due to the fact that the short-term results of an experiment do not necessarily match the theoretical probability. The law of large numbers states that as the number of repetitions of an experiment is increased, the observed relative frequencies of heads will tend to become closer to the theoretical probability of 0.5.

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Answer:

Step-by-step explanation:

Triangle ABC is a right angle triangle.

From the given right angle triangle,

AB represents the hypotenuse of the right angle triangle.

With m∠A as the reference angle,

AC represents the adjacent side of the right angle triangle.

BC represents the opposite side of the right angle triangle.

To determine tan m∠A, we would apply the tangent trigonometric ratio.

Tan θ = opposite side/adjacent side. Therefore,

Tan A = √32/2 = (√16 × √2)/2

Tan A = (4√2)/2

Tan A = 2√2

The value of tan A is in the simplest radical form  [tex]2\sqrt{2}[/tex].

The exact value of tanA in the simplest radical form.

The value of tan A is determined by using the formula;

[tex]\rm TanA = \dfrac{Perendicular}{Base}\\\\[/tex]

Where Perpendicular = [tex]\sqrt{32}[/tex] and Base = 2

Substitute all the values in the formula;

[tex]\rm TanA = \dfrac{Perendicular}{Base}\\\\TanA = \dfrac{\sqrt{32}}{2}\\\\TanA = \dfrac{4}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}}\\\\TanA = 2\sqrt{2}[/tex]

Hence, The value of tan A is [tex]2\sqrt{2}[/tex].

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x= -13 , y=11

Step-by-step explanation:

Using elimination method, make the x variable equal to eliminate the variable

-3x - y = -28

2x+ 3y=7

2(-3x-y =28)

3(2x+3y=7)

-6x - 2y =56

6x +9y=21

Apply addition

7y = 77

y=77/7 = 11

Use the value of y=11 in  

2x+ 3y=7

2x +3(11) =7

2x +33 =7

2x=7-33

2x= -26

x= -26/2 = -13

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Answer:

[tex]2\frac{2}{3}\text{ ft}^3\approx 2.67\text{ ft}^3[/tex]

Step-by-step explanation:

We have been given that Martha has 8 cubic feet of putting soil in the 3 flowerpots. She wants to put the same amount of soil in each pot.

To find the amount of soil in each pot, we need to divide total soil (8 cubic feet) by number of pots (3) as shown below:

[tex]\text{Amount of soil in each pot}=\frac{8\text{ ft}^3}{3}[/tex]

[tex]\text{Amount of soil in each pot}=2\frac{2}{3}\text{ ft}^3[/tex]

[tex]\text{Amount of soil in each pot}=2.6666\text{ ft}^3[/tex]

[tex]\text{Amount of soil in each pot}\approx 2.67\text{ ft}^3[/tex]

Therefore, Martha needs to put approximately 2.67 cubic feet of soil in each flower pot.

To determine the amount of soil Martha puts in each flowerpot, divide the total cubic feet of soil (8) by the number of flowerpots (3), which results in approximately 2.67 cubic feet of soil per pot.

The question pertains to the division of cubic feet of soil into equal amounts across three flowerpots. To find out how many cubic feet of soil Martha should put in each flower pot, we simply divide the total amount of soil by the number of flowerpots. In this case, Martha has 8 cubic feet of soil to distribute evenly into 3 pots.

The calculation would be as follows:

Therefore, Martha can put approximately 2.67 cubic feet of soil in each flower pot.

Answer:

MA

Step-by-step explanation:

Answer:

Zscore = 0.5

Step-by-step explanation:

If we assume a normal distribution, we mean that the diameters of each tomato follow a normal distribution. This is N~ (0,1).

By that, we mean that the mean (μ) = 0 and variance ([tex]\sigma^{2}[/tex]) = 1. Thus, since we are told that one tomato was in the 50th percentile. This implies the median. And is 0.5. And if the distribution is normal, the mean and median and mode should be equal.

Thus:

==> Z score = [tex]\frac{x-\mu}{\sigma}[/tex] = [tex]\frac{0.5 - \mu}{\sigma} = \frac{0.5-0}{1} = 0.5[/tex]

Answer:

A group of students formed a circle during a game.The circumference of the circle was about 43.96 feet,and the diameter of the circle was 14 feet.Which expression best represents the value of π?

The expression which represents the value of π is option C from the attachment that is π = 43.96/14

Step-by-step explanation:

Given:

Circumference of the circle = 43.96 feet

Diameter f the circle = 14 feet

So,

We know that :

Circumference of the circle = [tex]2(\pi )r[/tex] or [tex](\pi)d[/tex]

Re-arranging the formula:

⇒ [tex](\pi)d = Circumference\ (C)[/tex]  

⇒ [tex](\pi )d =C[/tex]

⇒ [tex]\frac{\pi\times d}{d}=\frac{C}{d}[/tex]

⇒ [tex]\pi =\frac{C}{d}[/tex]

Plugging the numeric values:

⇒ [tex]\pi =\frac{43.96}{14}[/tex]

So the expression for π is 43.96/ 14,and option C is the correct choice.

The required expression for value of x is [tex]\frac{43.96}{14}[/tex].

Given that,

The circumference of the circle was about 43.96 feet,

And the diameter of the circle was 14 feet

We have to determine,

Which expression best represents the value of x.

According to the question,

Circumference of the circle = 43.96 feet

Diameter f the circle = 14 feet

Then,

Circumference of the circle = [tex]\pi \times d[/tex]

Let, [tex]\pi = x[/tex]

Circumference of the circle  [tex]= x d[/tex]

Circumference of the circle = 43.96 feet

Therefore,

[tex]= 43.96 = x\times 14\\\\= x = \frac{43.96}{14} \\\\[/tex]

Hence, The required expression for value of x is [tex]\frac{43.96}{14}[/tex].

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The measure of the angle R is [tex]m \angle R=69.4[/tex]

Explanation:

It is given that the lengths of the triangle are PQ = 8 and QR = 3

To find the angle of R using the opposite and adjacent side, we shall use the tangent formula.

[tex]\tan \theta=\frac{o p p}{a d j}[/tex]

where opp = 8 and adj = 3

Thus, substituting these values in the formula, we get,

[tex]\tan \theta=\frac{8}{3}[/tex]

Multiplying both sides by [tex]tan^{-1}[/tex], we get,

[tex]\theta=tan^{-1} (\frac{8}{3})[/tex]

Dividing, we get,

[tex]\theta=69.44[/tex]

Rounding off to the nearest tenth, we have,

[tex]\theta=69.4[/tex]

Thus, the measure of the angle R is [tex]m \angle R=69.4[/tex]

Answer:

27.5 in (69.85 cm)

Step-by-step explanation:

The normal growth rate for an infant after birth is 1 in per month.

After six month, the infant will be 27.5 in which is equivalent to 69.85 cm.

Answer:

The option x squared ( root index 4 start root x squared end root) is correct

Therefore the equivalent expression to the given expression is [tex]x^2\sqrt[4]{x^2}[/tex]

Step-by-step explanation:

Given expression is [tex]\sqrt[4]{x^{10}}[/tex]

To find the equivalent expression to the given expression :

[tex]\sqrt[4]{x^{10}}[/tex]

[tex]=\sqrt[4]{x^{8+2}}[/tex]

[tex]=\sqrt[4]{x^8.x^2}[/tex] ( using the property [tex]a^m.a^n=a^{m+n}[/tex] )

[tex]=\sqrt[4]{x^{2\times 4}.x^2}[/tex]

[tex]=\sqrt[4]{(x^2)^4x^2}[/tex] ( using the peoperty [tex]a^{mn}=(a^m)^n[/tex] )

[tex]=\sqrt[4]{(x^2)^4}\times \sqrt[4]{x^2}[/tex] ( using the property [tex]\sqrt{ab}=\sqrt{a}\times \sqrt{b}[/tex] )

[tex]=x^2\sqrt[4]{x^2}[/tex]

Therefore [tex]\sqrt[4]{x^{10}}=x^2\sqrt[4]{x^2}[/tex]

Therefore the equivalent expression to the given expression is [tex]x^2\sqrt[4]{x^2}[/tex]

The option "x squared (RootIndex 4 StartRoot x squared EndRoot)" is correct

That is [tex]x^2\sqrt[4]{x^2}[/tex] is correct

Answer:

the correct answer is A

Step-by-step explanation:

hope this helped

Answer:

The answer to your question is letter C (x + 7)

Step-by-step explanation:

Expression

                             x² + 5x - 14

Factor the expression

- Find two number that multiplied give -14 and that added give 5

- Find the prime factors of -14

                       -14    2

                       -  7   7

                         -1

-From the prime factors, we notice that these numbers are + 7 and -2

-             x² + 7x - 2x - 14

- Factor the expression

              (x + 7)(x - 2)