In the trapezium, a = 7cm , b = 10.4cm h = 6.7cmwork out the area of the trapezium

[tex]\bf \begin{array}{ccll} problems&minutes\\ \cline{1-2} 12&45\\ 20&x \end{array}\implies \cfrac{12}{20}=\cfrac{45}{x}\implies \cfrac{3}{5}=\cfrac{45}{x}\implies 3x=225 \\\\\\ x=\cfrac{225}{3}\implies x=75[/tex]

It takes 75 minutes to solve 20 math problems.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here it takes 45 minutes to solve 12 math problems thus to solve 1 math problem it will take t= 45/12

                                            =3.75 minutes

Thus to solve 20 math problems it will take t₂₀=3.75×20

                                                                            =75 minutes

Hence, It takes 75 minutes to solve 20 math problems.

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Answer:

−115.940465

Step-by-step explanation:

Simplified = −115.940465

Answer:

-4/3.

Step-by-step explanation:

Using the change of base formula  convert to  log 3:

logb x = loga x / loga b

log(1/27) 81 = log3 81 / log3 1/27

log3 81  = 4 ( because 3^4 = 81) and log3 1/27 = -3 (because 3^-3 = 1/27)

So  log(1/27) 81 = 4/-3 = -4/3.

Answer:

70

Step-by-step explanation:

50+20 = 70

ANSWER

70

EXPLANATION

We want to increase 50 by 40%

Method 1

New amount =50+40% of 50

[tex] = 50 + \frac{40}{100} \times 50[/tex]

[tex] = 50 + \frac{40}{2} [/tex]

[tex] = 50 + 20[/tex]

[tex] = 70[/tex]

Method 2.

50 corresponds to 100%.

New amount corresponds to (100+40=140)%

This implies that, New amount

[tex] = 140\% \times 50[/tex]

[tex] = \frac{140}{100} \times 50[/tex]

[tex] = \frac{140}{2} [/tex]

[tex] = 70[/tex]

Final answer:

The best first step to simplify the equation -2(x+3)=-10 is to distribute the -2 to the terms inside the parentheses and simplify. Then, solve for x by isolating the variable.

Explanation:

The best first step to simplify the equation -2(x+3)=-10 is to distribute the -2 to the terms inside the parentheses. This can be done by multiplying -2 with each term inside the parentheses.

So, -2(x+3) becomes -2x-6. The equation now becomes -2x - 6 = -10.

Now, we can proceed with solving the equation by isolating the variable x.

We can begin by adding 6 to both sides of the equation to get -2x = -4.

Finally, we divide both sides of the equation by -2 to solve for x.

So, x = 2.

The correct answer is option c. [tex]\frac{-2}{\ 2}(x+3) = \frac{-10}{\ 2}[/tex]

When solving the equation -2(x+3)=-10, the best first step is to divide both sides by 2. This simplifies the equation by making it easier to solve.

Here are the steps:

By dividing first, you simplify the algebraic manipulation and make solving the equation straightforward.

The complete question is:
When solving equation which is the best first step to begin to simplify the equation -2(x+3)=-10

a. [tex](-2)(-2)(x+3) = -10(-2)[/tex]

b. [tex]\frac{-1}{\ 2}(-2)(x+3) = (-10)\frac{-1}{\ 2}[/tex]

c. [tex]\frac{-2}{\ 2}(x+3) = \frac{-10}{\ 2}[/tex]

d. [tex]\frac{-2}{-10}(x+3) = \frac{-10}{-10}[/tex]

Answer:

2

Step-by-step explanation:

3(2x + 4)=?

6x + 12

6x/6=x

12/6=2

x=2

Answer:

SLOPE = -5

Step-by-step explanation:

Because that's what x is.

Answer:

1.    2x(-3x - 1)

-6x^2 - 2x

2.   -x(4 + 2x)

-4x - 2x^2

3.   -5x(-2x + 4)

10x^2 - 20x

4.   x(-2x - 2) + 3(-4x - 6x)

-2x^2 - 2x - 12x - 18x

-2x^2 - 32x

5.   2xy(-3x - 5y) + 4y(-2xy - 4x)

-6x^2y - 10xy^2 -8xy^2 - 16yx

-6x^2y -18xy^2 - 16yx

You just distribute (multiply) what's outside the parentheses with everything inside the parentheses.  Then, combine like terms.

Answer:

1.    2x(-3x - 1)

-6x^2 - 2x

2.   -x(4 + 2x)

-4x - 2x^2

3.   -5x(-2x + 4)

10x^2 - 20x

4.   x(-2x - 2) + 3(-4x - 6x)

-2x^2 - 2x - 12x - 18x

-2x^2 - 32x

5.   2xy(-3x - 5y) + 4y(-2xy - 4x)

-6x^2y - 10xy^2 -8xy^2 - 16yx

-6x^2y -18xy^2 - 16yx

Answer:

999

 530

+469

----------

 999

Answer:

[tex]m<1=26.4\°[/tex]

[tex]m<2=153.6\°[/tex]

Step-by-step explanation:

we know that

If m<1 and m<2 form a linear pair

then

[tex]m<1+m<2=180\°[/tex] -----> by supplementary angles

substitute the values and solve for x

[tex](2x+20)+48x=180\°[/tex]

[tex]50x=180\°-20\°[/tex]

[tex]50x=160\°[/tex]

[tex]x=3.2\°[/tex]

Find the measure of each angle

[tex]m<1=(2x+20)=2(3.2\°)+20\°=26.4\°[/tex]

[tex]m<2=48x=48(3.2\°)=153.6\°[/tex]

➷ The perimeter is the sum of all the lengths

206 - (59 + 94) = 53

It is 53 inches.

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

53 inches.

Step-by-step explanation:

Perimeter =  sum of the 3 sides so the third side

= 206 - 94 - 59 = 53.

Answer:

[tex]\large\boxed{Q4.\ C.\ \text{Infinitely Many Solutions}}\\\boxed{Q5.\ D.\ \text{No Solution}}[/tex]

Step-by-step explanation:

[tex]Q4.\\\\\left\{\begin{array}{ccc}-4y+4=x&(1)\\2x+8y=8&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\2(-4y+4)+8y=8\qquad\text{divide both sides by 2}\\-4y+4+4y=4\qquad\text{combine like terms}\\4=4\qquad\bold{TRUE}\\\\\text{Infinitely Many Solutions}[/tex]

[tex]Q5.\\\\\left\{\begin{array}{ccc}6x+2=y&(1)\\3y-18x=12&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\3(6x+2)-18x=12\qquad\text{divide both sides by 3}\\6x+2-6x=4\qquad\text{combine like terms}\\2=4\qquad\bold{FALSE}\\\\\text{No Solution}[/tex]

Answer:

36

Step-by-step explanation:

1. 48 divided by 3= 12

2. 12 x 3= 36

48 students in group 2

43 students in group 1

So in total there are 91 students

7 students play the trump

And 20 play the trombone

Therefore it is known that 27 students play those two instruments in total

Because of this, Subtract 27 from 91 to get the num of students who doesn't play those instruments.

Answer:

See below

Step-by-step explanation:

What the significance level tells us is that, in this case, there is only a 5% chance that the change in results from the sample happened by random chance.  So that means that most likely the change in results did not happen by random change, and something happen between the times the samples were taken.  In this case, the experiment.

P = 0.05 means that the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed, is 0.05.

P = 0.05 does not represent the probability that the null hypothesis is true or false, nor does it signify that the outcome is 5% higher in one group compared to the other. Instead, P = 0.05 is the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as the one observed. In simpler terms, it indicates the likelihood of obtaining the observed results, or results more extreme, under the assumption that there is no true effect or difference between the groups.

In hypothesis testing, researchers start with a null hypothesis (H0) that states there is no effect or difference between the groups being compared. The alternative hypothesis (Ha), on the other hand, posits that there is a significant effect or difference. The p-value quantifies the strength of evidence against the null hypothesis. A low p-value (such as P = 0.05) suggests that the observed results are unlikely to have occurred by chance alone, leading to the rejection of the null hypothesis in favor of the alternative hypothesis.

When a study reports a statistically significant improvement in Verbal GRE performance with P = 0.05, it means that the probability of obtaining the observed improvement (or a more significant one) under the assumption of no actual effect is 5% or less. Therefore, there is strong evidence to suggest that the technique used in the experiment does indeed have a positive impact on students' Verbal GRE scores.

To know more about probability here

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The password format is = inpray93

vowel , consonant, consonant, consonant, vowel, consonant, number, number.

There are 21 consonants, 5 vowels and 10 number choices (0-9)

Since, there are 21 consonants and repetition is allowed so for 2nd, 3rd, 4th, and 6th positions 21 choices are available. For 1st and 5th positions, 5 choices  are available and for 7th and 8th position there are 10 choices (0 to 9).

Passwords are not case sensitive which means upper case and lower case letters are same.

So, the number of passwords can be =

[tex]5\times21\times21\times21\times5\times21\times10\times10[/tex]

= 486202500

Part (b) question is not given. But it can be opposite to the first part i.e when the password letters are case sensitive.

This means all the letters are different.

So, number of passwords will be =

[tex]10\times42\times42\times42\times10\times42\times10\times10[/tex]

= 31116960000

Answer:

26

Step-by-step explanation:

Let his age = x

Equation

x - 12 = 14            

Solution

Add 12 to both sides.

x - 12 +12 = 14 + 12

x = 26

He is currently 26 years old.

Length:width

6 inches: 1 inch

30 inches: 5 inches

Since the ratio for length is multiplied by 5, you would do the same for width.

Answer:

[tex]\large\boxed{Q\#1.\ A)\ \dfrac{8}{3}x+6}\\\boxed{Q\#2.\ A)\ \dfrac{1}{3}(p+45)}[/tex]

Step-by-step explanation:

[tex]Q\#1:\\\\\dfrac{2}{3}(4x+9)\qquad\text{use the distributive property}\\\\=\left(\dfrac{2}{3}\right)(4x)+\left(\dfrac{2}{3}\right)(9)=\dfrac{8}{3}x+(2)(3)=\dfrac{8}{3}x+6\\\\Q\#2:\\\\\dfrac{1}{3}p+15=\dfrac{1}{3}p+\dfrac{1}{3}\cdot(3)(15)=\dfrac{1}{3}p+\dfrac{1}{3}\cdot45=\dfrac{1}{3}(p+45)[/tex]

he is still looking for seven more flowers

Answer:

The answer is n, greater than or less than 13.

Answer:

option 2

2x²- x - 1

Step-by-step explanation:

We are given points: (-1,2), (0,-1) and (2,5)

Substitute each point one by one in the quadratic equation to check if the quadratic equation contains all points mention.

2) f(x) = 2x²- x - 1

   Point(-1,2)

   f(-1) = 2(-1)² -(-1) -1

   2 = 2 + 1 - 1

   2 = 2

  Point(0,-1)

   f(0) = 2(0)² -(0) -1

   -1 = 0 - 0 -1

   -1 = -1

  Point(2,5)

  f(2) = 2(2)² -(2) -1

  5 = 8 - 2 -1

  5 = 6 - 1

  5 = 5    

This would be D cause these are 30,60, 90 angles. 30 (X) 60(X square root of 3 and 90 2x).

Answer:

C

Step-by-step explanation:

Using the sine ratio on the right triangle on the right side

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{8}[/tex]

Multiply both sides by 8 × sin30° = y

⇒ y = 8 × [tex]\frac{1}{2}[/tex] = 4 → C

Answer: option d.

Step-by-step explanation:

You have the following formul given in the problem:

[tex]p=1-e^{-mt}[/tex]

You know that:

The number of  customers serviced in an hour by the technical support representative is 6 costumbers, therefore:

[tex]m=6[/tex]

As the problem asked for the probability that  a costumber will be on hold less than 30 minutes, we know that:

[tex]t=0.5[/tex]

Substitute the values above into the formula.

Then, you obtain:

[tex]p=1-e^{-(6)(0.5)}=0.95[/tex] or 95%

Answer:

Linear

Step-by-step explanation:

Hello

Is linear

Best regards

Answer:

Linear

Step-by-step explanation:

Linear function : if the value increases with the constant value per period,

It can written as y = a + bx

Where, a = initial value, b = constant value per period,

Exponential function :  if the value increases with the constant rate per period,

It can be written as,

[tex]y=ab^x[/tex]

Where, a = initial value, b = growth factor per period.

∵ Every year 39 million cars cross the Golden Gate Bridge in San Francisco.

Then after x years, the number of cars ( in million )

f(x) = 39x

⇒ f(x) = 0 + 39x

By the above explanation,

Hence, the function that represents the number of cars that have crossed the Golden Gate Bridge is linear.

Answer:

The second option.

3x + 6 = 21.

Step-by-step explanation:

3x + 6 = 21.

If x = 5, plug it in.

3 · 5 + 6 = 21

15 + 6 = 21

Hope this helps,

Davinia.

Answer:

Second Option

Step-by-step explanation:

Answer:

[tex]\large\boxed{P=(16+36x)\ ft}[/tex]

Step-by-step explanation:

The formula of an area of a rectangle:

[tex]A=bh[/tex]

b - base

h - height

We have A = 144x ft² and h = 8. Substitute and solve for b:

[tex]144x=8b[/tex]              divide both sides by 8

[tex]b=18x\ ft[/tex]

The formula of a perimeter of a rectangle:

[tex]P=2b+2h[/tex]

Substitute:

[tex]P=2(18x)+2(8)=36x+16[/tex]

Final answer:

To find the two numbers whose sum is 16 and difference is 20, we set up two equations from the given conditions and solve them simultaneously, yielding the numbers 18 and -2.

Explanation:

The student has asked about solving a system of equations where the sum of two numbers is 16 and their difference is 20. We can set up two equations based on the given information:

x + y = 16 (Equation 1, where x and y are the two numbers)

x - y = 20 (Equation 2, because the difference between the two numbers is 20)

To find the two numbers, we can solve this system of equations by adding both equations to eliminate the 'y' variable:

2x = 36

Dividing both sides by 2 gives us x = 18. We then substitute x back into Equation 1 to find y:

18 + y = 16 => y = 16 - 18 => y = -2

Therefore, the two numbers are 18 and -2.

Answer:

1/15

Step-by-step explanation:

You have a 1/3 chance of being an elf.

You have a 1/5 change of having the magic tool.

1/3 × 1/5 = 1×1/3×5 = 1/15

Answer:

it is 1/15

Step-by-step explanation: