PLEASE HELP!!!!
This year, the Nature Club made 3 exhibits per month for its annual fair. This year's fair has twice as many exhibits as last year's. How many exhibits were there in last year's fair?

Answer:

c = 10

Explanation:

Use Pythagoras theorem: a² + b² = c²

where 'a' and 'b' are legs and 'c' is the hypotenuse (the longest side)

Here given: a = 8 cm, b = 6 cm, c = ?

Substituting values:

8² + 6² = c²

c² = 64 + 36

c² = 100

c = √100

c = 10

Answer:

10 cm

Step-by-step explanation:

[tex]a^2=b^2+c^2[/tex]

[tex]a^2=6^2+8^2[/tex]

[tex]a^2=100[/tex]

[tex]\sqrt{a^2}=\sqrt{100[/tex]

a=10

Answer:   [tex]\log_2(20)[/tex]

Work Shown:

[tex]\log_2(4) + \log_2(5)\\\\\log_2(4*5)\\\\\log_2(20)\\\\[/tex]

The rule used is [tex]\log_{b}(\text{x}) + \log_{b}(\text{y}) = \log_{b}(\text{xy})[/tex]

[tex]\large{\textbf{Heya !}}[/tex]

✏[tex]\large\sf{\bigstar Given:-}[/tex] ✏

✏[tex]\large{\sf{\bigstar To\quad Find:-}[/tex] ✏

✏[tex]\large{\sf{\bigstar Solution\quad steps:-}[/tex]

`To find what we want we need to apply ㏒ rules

[tex]\large{\sf{\longmapsto{log_ba+log_bc=log_b(ac)}[/tex]

using formula,

[tex]\large{\sf{\longmapsto{log_24+log_25=log_2(4\cdot5)}[/tex]

simplifying,

[tex]\large{\sf{\longmapsto{log_220}[/tex]

`hope it was helpful ! ~

Answer:

9cm

Step-by-step explanation:

If the triangles are similar then their lengths are in a ratio to each other, Ex: PR is 3 times LN, 2*3 = 6cm

This gives us a ratio of 1:3

PQ = LM*3 = 3cm*3 = 9cm

The complete proof of the theorem is

Statements                                     Reasons

1. p||q                                               1. Given

2. ∠1≅∠3                                         2. Alternate interior angles theorem

3. ∠1≅∠3                                        3. Definition of congruent angles

4. ∠3 + ∠2 ≅ 180°                          4. Definition of linear pair

5. m∠3 + m∠2 = 180°                      5. Linear pair theorem

6. m∠1 + m∠2 = 180°                     6. Substitution prop. of equality

7. ∠1 and ∠2 are supplementary  7. Consecutive interior angles theorem

From the question, we are to complete the given proof

The proof is completed as shown below

Statements                                     Reasons

1. p||q                                               1. Given

2. ∠1≅∠3                                         2. Alternate interior angles theorem

3. ∠1≅∠3                                        3. Definition of congruent angles

4. ∠3 + ∠2 ≅ 180°                          4. Definition of linear pair

5. m∠3 + m∠2 = 180°                      5. Linear pair theorem

6. m∠1 + m∠2 = 180°                     6. Substitution prop. of equality

7. ∠1 and ∠2 are supplementary  7. Consecutive interior angles theorem

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Answer:

AC = 23

Step-by-step explanation:

Discussion

AB and AC start from the same point -- A.

That means that when speaking of tangents to a circle that AB = AC

Answer

AB = 23 in          Given

AC = 23              2 tangents to a circle starting from the same point are =

Answer:

[tex]b^{2} +7b+7[/tex] with remainder 1

The interpretation of the point of intersection of the curves is (c) they give a solution to the equation 5x - x^2 = 3x - 0.5x^2

The graph of the two functions alongside their equations are the given parameters of this question

The functions are given as:

f(x) = 5x - x^2

g(x) = 3x - 0.5x^2

When the graphs of two curves or lines intersect on a coordinate plane, it means that the point of intersection represents where the graphs have equal value

In this case, it represents

f(x) = g(x)

Substitute the known values in the above equation

5x - x^2 = 3x - 0.5x^2

So, the interpretation of the point of intersection of the curves is (c) they give a solution to the equation 5x - x^2 = 3x - 0.5x^2

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2 photos will not be displayed

The given parameters are:

Photos = 17

Rows = 3

Divide 17 by 3 and take note of the remainder

Photos left = 17/3

This gives

Photos left = 5 remainder 2

Hence, 2 photos will not be displayed

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Answer: 9

Step-by-step explanation:

Answer:

9 songs

Step-by-step explanation:

a quarter is basically a fourth of a number so you need to just divide the number by four

The data of the customer responses would be classified as ordinal data.

Ordinal data is a category of categorical data that has a predetermined order or scale. Ordinal data, for instance, is said to have been gathered when a respondent rates their level of financial contentment on a scale from 1 to 10. There is no established scale for measuring the variance of each score in ordinal data.

Ordinal data is a categorical statistical data type when the distances between the categories are unknown and the variables have naturally occurring, ordered categories. On an ordinal scale, these data are available. By having a ranking, the ordinal scale differs from the nominal scale.

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1) [tex]\overline{WX} \cong \overline{UY}[/tex], [tex]\angle YXZ \cong \angle XYZ[/tex] (given)

2) [tex]\overline{XY} \perp \overline{XY}[/tex] (reflexive property)

3) [tex]\triangle WXY \cong \triangle UYX[/tex] (SAS)

4) [tex]\overline{WY} \perp\overline{ UX}[/tex] (CPCTC)

The value of Mario's car after 5 years is $8,249.

Deprecation is when the value of an asset declines with the passage of time as a result of wear and tear.

V = 15,999 − 1,550t

V = 15,999 − 1,550(5)

V = 15,999 - 7,750

V =$8,249

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Answer:

m = [tex]\frac{1}{2}[/tex] , m = 5

Step-by-step explanation:

assuming you mean

2m² - 11m + 5 = 0

consider the product of the factors of the m² term and the constant term which sum to give the coefficient of the m- term

product = 2 × 5 = 10 and sum = - 11

the factors are - 10 and - 1

use these factors to split the m- term

2m² - 10m - m + 5 = 0 ( factor the first/second and third/fourth terms )

2m(m - 5) - 1(m - 5) = 0 ← factor out (m - 5) from each term

(m - 5)(2m - 1) = 0 ← in factored form

equate each factor to zero and solve for m

2m - 1 = 0 ⇒ 2m = 1 ⇒ m = [tex]\frac{1}{2}[/tex]

m - 5 = 0 ⇒ m = 5

Answer:

1. Translate 5 units up (Fixed after a comment from subtomex0 - Thanks again!)

2. Vertical Compression by a scale factor of 3/8

3. Reflect across the y-axis, and shift 2 units to the left

4. Vertical stretch by a scale factor of 6, and shifting 1 unit up

5. Shifting 11 units to the left

6. Vertical stretch by a scale factor of 8

7. Vertical compression by a scale factor of 1/2, and reflection across the y-axis.

Total number of five letter strings formed by A,B,C and D with repetitions allowed

={4x4x4x4x4 = 4 power 5 = 1024

Now, fix BAD in a string at one place then we have 2 more places to be filled with 4 letters, total number of such strings

=4x4=16

Here, BAD can be at any of the 3 positions,

Hence the total number of strings with BAD in it

= 3 x 16=48

Now, The total number of strings not containing BAD

=1024-48

=976

Using 26 letters, the number of 5-letter words that can be formed when the letters are different is determined as follows: 26P5 = 26 × 25 × 24 × 23 × 22 = 7883600 different words.

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Answer:

x=4 and y=−9

Step-by-step explanation:

Problem:

Solve 7x+4y=−8;−8x−5y=13

Steps:

I will solve your system by substitution.

(You can also solve this system by elimination.)'

7x+4y=−8;−8x−5y=13

Step: Solve 7x+4y=−8 for x:

7x+4y+−4y=−8+−4y(Add -4y to both sides)

7x=−4y−8

7x/7 =  -4y-8/7 (Divide both sides by 7)

x=-4/7y + -8/7

Step: Substitute -4/7y + -8/7 for x in −8x−5y=13:

−8x−5y=13

-8(-4/7y + -8/7) −5y=13

-3/7y + 64/7 =13(Simplify both sides of the equation)

-3/7y + 64/7 + -64/7 = 13 + -64/7 (Add (-64)/7 to both sides)

-3/7y = 27/7

-3/7y/-3/7 = 27/7/-3/7 (Divide both sides by (-3)/7)

y=−9

Step: Substitute −9 for y in x= -4/7y + -8/7:

x = -4/7y + -8/7

x = -4/7 (-9) + -8/7

x=4(Simplify both sides of the equation)

Answer:

x=4 and y=−9

The total mass of Adrian and Chang at birth is 7.41 kilograms

Total mass of the babies = Adrian weight + Chang weight

= 2.87 kilograms + 4.54 kilograms

= 7.41 kilograms

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The total number of small drinks 's' bought by Maria is 7.

The total number of medium drinks 'm' drinks bought by Maria is 6.

A collection of one or more linear equations containing the same variables is known as a system of linear equations (or linear system).

Formation of the linear equation for the drinks bought by Maria:

The total number of drinks bought by the Maria is 13.

Lets say 'm' represents the number of medium drink.

's' represents the number of small drink.

Total drinks comprises of medium drinks and small drinks.

Thus,

s + m = 13, is the first linear equation.

Now medium drinks cost $3.

Total cost for purchasing medium drinks = (price of one medium drink)×(total number of medium drinks)

Total price for medium drinks = 3×m

Similarly,

Total cost for purchasing small drinks = (price of one small drink)×(total number of small drinks)

Total price for small drinks = 2×s

Total cost = total cost of medium drink + total cost of small drink

          32  = 3×m + 2×s, is second linear equation.

From equation first substitute the value of 'm' in second equation to fine the total number of drink.

32 = 3×(13 - s) + 2×s

32 = 39 - 3s + 22

s = 7

Put s = 7 in first equation and calculate 'm'.

m = 13 -7

m = 6

Therefore, The total number of small drinks 's' bought by Maria is 7.

The total number of medium drinks 'm' drinks bought by Maria is 6.

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The growth factor as a decimal is 1.026 and the number of students enrolled 10 years from now is 1939

The given parameters are

Initial value of enrollment, a = 1500

Rate, r = 2.6%

The growth factor is then calculated as:

Growth factor = 1 + Rate

This gives

Growth factor = 1 + 2.6%

Evaluate the sum

Growth factor = 1.026

Hence, the growth factor as a decimal is 1.026

As a general rule, the number of students enrolled t years from now is

Students = Initial value * Growth factor^Number of years

This is represented as

Students = 1500(1.026)^t

10 years from now means t = 10

So, we have

Students = 1500(1.026)^10

Evaluate

Students = 1939

Hence, the number of students enrolled 10 years from now is 1939

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There are 11 prime dates in it.

The prime numbers between 1 and 30 are 1, 2,3,5,7,11,13,17,19,23,29

Relative prime:

Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.

Hence There are 11 prime dates in the month of June.

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Answer: 10

Step-by-step explanation:

Since exactly 1 in every $n$ consecutive dates is divisible by $n$, the month with the fewest relatively prime days is the month with the greatest number of distinct small prime divisors. This reasoning gives us June ($6=2\cdot3$) and December ($12=2^2\cdot3$). December, however, has one more relatively prime day, namely December 31, than does June, which has only 30 days. Therefore, June has the fewest relatively prime days. To count how many relatively prime days June has, we must count the number of days that are divisible neither by 2 nor by 3. Out of its 30 days, $\frac{30}{2}=15$ are divisible by 2 and $\frac{30}{3}=10$ are divisible by 3. We are double counting the number of days that are divisible by 6, $\frac{30}{6}=5$ days. Thus, June has $30-(15+10-5)=30-20=\boxed{10}$ relatively prime days.

Step-by-step explanation:

gallons to quarts have the ratio 1:4.

there are 4 quarts in a gallon (hence the name of quarts by the way).

so, the question is really, which order pair have also a 1:4 ratio between x and y ?

(1, 4)

(2, 8)

(3, 12)

the (4, 1) would represent a 4:1 ratio.

and as you know, 4/1 is different to 1/4.

a ratio is nothing else than a fraction. just the "whole" is different.

the pure fraction 1/4 means that the whole is 4/4, has 4 times 1/4.

a ratio 1:4 (you can also write as 1/4) means that the whole has 5 (1+4) parts.

other than that they are compared and calculated with the same way as normal fractions.

Applying the angle of intersecting secants theorem, the measure of angle B is: 35°.

The measure of the angle formed outside a circle by two intersecting secants is equal to half the positive difference of the measures of the arcs they intercept based on the angle of intersecting secants theorem.

Applying the angle of intersecting secants theorem, we have the following:

Let the missing measure of the arc for angle A be x. Therefore:

6 = 1/2(x - 17)

2(6) = x - 17

12 = x - 17

12 + 17 = x

x = 29°

m∠B = 1/2(99 - x)

Plug in the value of x

m∠B = 1/2(99 - 29)

m∠B = 35°

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The distance travelled is 10 m

The velocity gained at the end of the time is 2 m/s

From the question, we are to determine distance travelled and the velocity gained

From one of the equations of motion for linear motion, we have that

S = ut + 1/2at²

Where S is the distance

u is the initial velocity

t is the time taken

and a is the acceleration

First, we will calculate the acceleration

Using the formula,

F = ma

Where F is the force

m is the mass

and a is the acceleration

∴ a = F/m

Where F is the force

and a is the acceleration

From the given information,

F = 50 N

m = 250 kg

Putting the parameters into the equation,

a =  50/250

a = 0.2 m/s²

Thus,

From the information,

u = 0 m/s (Since the object was initially at rest)

t = 10 s

S = 0(t) + 1/2(0.2)(10)²

S = 10 m

Hence, the distance travelled is 10 m

For the velocity

Using the formula,

v = u + at

Where v is the velocity

v = 0 + 0.2×10

v = 2 m/s

Hence, the velocity gained at the end of the time is 2 m/s

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The probability that a randomly grab 2 extra large jerseys is 18.3%.

Given that a box of jerseys for a pick-up game of basketball contains 8 extra-large jerseys, 6 large jerseys, and 4 medium jerseys.

The number of jerseys in the box is 8+6+4=18

To find the probability of picking 2-extra large jerseys by finding the probability of 1 extra large and probability of 2 extra large.

The probability of picking 1 extra large jersey is

P₁=8/18

P₁=4/9

The probability of picking 2 extra large jerseys is remaining jerseys

P₂=7/17

The total probability of getting 2 extra large jerseys is

P=P₁×P₂

P=(4/9)×(7/17)

P=28/153

P=0.183

P=18.3%

Hence, the probability that randomly grab 2 extra-large jerseys when basketball contains 8 extra-large jerseys, 6 large jerseys, and 4 medium jerseys is 18.3%.

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If Angle A ≅ Angle T, then the triangles would be congruent by ASA

If Angle B ≅ Angle P, then the triangles would be congruent by AAS.

We are told that;

Sides AC and TQ are congruent.

Angles BCA and  PQT are congruent.

Thus, we can say that;

Side AC and side TQ are congruent.

Angle BCA and angle PQT are congruent too.

Since angle A and angle T are congruent, it means the congruency theorem used will be ASA(Angle - Side - Angle) Theorem.

Lastly, if angle B were to be congruent to angle P,  it means the congruency theorem used will be AAS(Angle - Angle - Side) Theorem.

The missing options are;

A) If AngleA ≅ AngleT, then the triangles would be congruent by ASA.

B) If AngleB ≅ AngleP, then the triangles would be congruent by AAS.

C) If all the angles are acute, then the triangles would be congruent.

D) If AngleC and AngleQ are right angles, then triangles would be congruent.

E) If BC ≅ PQ, then the triangles would be congruent by ASA.

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Using the z-distribution, the confidence interval is given by: (11.95, 12.65).

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

The other parameters are given as follows:

[tex]\overline{x} = 12.3, \sigma = 1.5, n = 50[/tex]

Hence the bounds of the interval are:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 - 1.645\frac{1.5}{\sqrt{50}} = 11.95[/tex]

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 + 1.645\frac{1.5}{\sqrt{50}} = 12.65[/tex]

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The mean of the distribution given is 0.569.

Given some distribution like under:

     x                           p(x)

     0                            0.650

     1                             0.216

     2                             0.087

     3                             0.026

     4                             0.014

      5                            0.009

We have to find the mean of the distribution.

Mean is the sum of numbers divided by the numbers which are taken into consideration. It is also known as average.

Mean=sum/n

To find the mean of distribution we have to find sum of x*p(x)

∑xp(x)=0*0.650+1*0.216+2*0.0087+3*0.026+4*0.014+5*0.009

=0+0.216+0.174+0.078+0.056+0.045

=0.569

Hence the mean of the distribution given in the question is 0.569.

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Distribution in the given question is wrong and the right question is as the right distribution is as under:

 x                           p(x)

     0                            0.650

     1                             0.216

     2                             0.087

     3                             0.026

     4                             0.014

     5                            0.009

158/4 as a mixed number in the simplest term is  [tex]39\frac{3}{4}[/tex]

The given fraction is 158/4

The number of times that 158 can be divided by 4 = 39

4 x 39 = 156

The remainder = 159 - 156

The remainder = 3

The mixed number is of the form:

[tex]Quotient\frac{Remaider}{Divisor}[/tex]

Therefore, the mixed number is [tex]39\frac{3}{4}[/tex]

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The analysis which would be most appropriate for randomly assign people to one of three experimental conditions (Treatment A, Treatment B, Control) are-

A statistical test called an analysis of variance, or ANOVA, is used to compare the means of more than two groups.

A helpful framework for analysing how various variables affect various continuous variables is the general linear model (GLM).

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The complete question is -

Suppose you are performing an experiment where you randomly assign people to one of three experimental conditions (Treatment A, Treatment B, Control). Which analysis would be most appropriate?