Simplify the expression.
(7-6)(-1)
-7 +0
-7-
7-6
7+ c

Answer:

here,

a=b+12

b=a-12----> equation (i)

b= c+4

putting the value of b from the equation (I)

a-12=c+4

a=c+4+12

a=c+16

hope this helps...

Good luck on your assignment...

The value of a + c is 16.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

a=b+12

So, b=a-12 ---- equation (i)

and, b= c+4

Substitute the value of b from the equation (I)

a-12=c+4

a=c+4+12

a=c+16

Hence, the value of a+ c is 16.

Learn more about Algebra here:

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Answer:

1140 ways.

Step-by-step explanation:

The applicable formula is: (n +r - 1)C(r-1), where n is the number of identical items (the candies), and r is the possible number of recipients (the kids).

The 17 identical candies, can be distributed among the 4 children in :  

=(17 + 4 - 1)C(4–1) = 20C3 ways.

= 20!/((20–3)!*3!) ways.

= 20*19*18*17!/(17!*(3*2*1)) = 20*19*18/6 ways

= 20*19*3 ways.  

=1140 ways.

Answer:

Option B

Step-by-step explanation:

Again, another great question! Here we are given the following system of equations, bound by quadrant 1 -

[tex]\begin{bmatrix}2x+7y\le \:70\\ 8x+4y\le \:136\end{bmatrix}[/tex]

Convert this to slope - intercept form -

[tex]\begin{bmatrix}y\le \frac{70-2x}{7}\\ y\le \:2\left(-x+17\right)\end{bmatrix}[/tex]

Now the graphed solution of this intersects at a shaded region with which there are 3 important point that lie on the border. They are the following -

( 0, 10 ),

( 15, 9 ),

( 17, 0 )

When these point are plugged into the main function f ( x, y ) = 2x + 6y, the point ( 15, 9 ) results in the greatest solution of 84. Thus, it is our maximum point -

Option B

Answer:

m∠A = 17 degrees       m∠B = 73 degrees     m∠C = 90 (given)    a =   12 (given)    b =  40           c = 42 (given)

Step-by-step explanation:

Use sin to solve m∠A

sin x = 12/42     Simplify

sin x = 0.2857   Use the negative sin to solve for x

sin^-1 x =  17 degrees

Add together all of the angle measures to solve for m∠B

17 + 90 + x = 180    Add

107 + x = 180

-107        -107

x = 73 degrees

Use Pythagorean Theorem to solve for b

12^2 + x^2 = 42^2     Simplify

144 + x^2 = 1764

-144            -144

x^2 = 1620               Take the square root of both sides

x = 40

Answer:

d. 0.459 < p < 0.603

Step-by-step explanation:

We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.531.

[tex]p=X/n=69/130=0.531[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.531*0.469}{130}}\\\\\\ \sigma_p=\sqrt{0.001916}=0.044[/tex]

The critical z-value for a 90% confidence interval is z=1.645.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.044=0.072[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.531-0.072=0.459\\\\UL=p+z \cdot \sigma_p = 0.531+0.072=0.603[/tex]

The 90% confidence interval for the population proportion is (0.459, 0.603).

Answer:

For lines A and B to be parallel, the Same Side Interior angles must be supplementary which means:

2x + 10 + 4x + 80 = 180

6x + 90 = 180

6x = 90

x = 15°

Answer:

1. The 99% confidence interval is from 941.527 to 958.473

2. The 99% confidence interval is from 933.054 to 966.946

3. The 99% confidence interval is from 916.108 to 983.892

Step-by-step explanation:

The confidence interval is given by

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]

Where [tex]\bar{x}[/tex] is the sample mean and Margin of error is given by

[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]

Where n is the sample size,

s is the sample standard deviation,

[tex]t_{\alpha/2[/tex] is the t-score corresponding to some confidence level

The t-score corresponding to 99% confidence level is

Significance level = α = 1 - 0.99 = 0.01/2 = 0.005

Degree of freedom = n - 1 = 13 - 1 = 12

From the t-table at α = 0.005 and DoF = 12

t-score = 3.055

1. 99% Confidence Interval when s = 10

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{10}{\sqrt{13} } \\\\MoE = 3.055\cdot 2.7735\\\\MoE = 8.473\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 8.473\\\\\text {confidence interval} = 950 - 8.473, \: 950 + 8.473\\\\\text {confidence interval} = (941.527, \: 958.473)\\\\[/tex]

The 99% confidence interval is from 941.527 to 958.473

2. 99% Confidence Interval when s = 20

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{20}{\sqrt{13} } \\\\MoE = 3.055\cdot 5.547\\\\MoE = 16.946\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 16.946\\\\\text {confidence interval} = 950 - 16.946, \: 950 + 16.946\\\\\text {confidence interval} = (933.054, \: 966.946)\\\\[/tex]

The 99% confidence interval is from 933.054 to 966.946

3. 99% Confidence Interval when s = 40

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{40}{\sqrt{13} } \\\\MoE = 3.055\cdot 11.094\\\\MoE = 33.892\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 33.892\\\\\text {confidence interval} = 950 - 33.892, \: 950 + 33.892\\\\\text {confidence interval} = (916.108, \: 983.892)\\\\[/tex]

The 99% confidence interval is from 916.108 to 983.892

As the sample standard deviation increases, the range of confidence interval also increases.

Answer: 5182

To get the value of all 100 numbers you would need to multiply.

Step-by-step explanation:

51.82x100= 5182

Answer:

  41°, 56°, 83°

Step-by-step explanation:

We can find the largest angle from the law of cosines:

  c² = a² +b² -2ab·cos(C)

  C = arccos((a² +b² -c²)/(2ab))

  C = arccos((4² +5² -6²)/(2(4)(5))) = arccos(5/40) ≈ 82.8192°

Then the second-largest angle can be found the same way:

  B = arccos((4² +6² -5²)/(2·4·6)) = arccos(27/48) ≈ 55.7711°

Of course the third angle is the difference between the sum of these and 180°:

  A = 180° -82.8192° -55.7711° = 41.4096°

Rounded to the nearest degree, ...

  the angles of the triangle are 41°, 56°, 83°.

Answer:

Option (C)

Step-by-step explanation:

Given expression is,

[tex]4+4\times \text{log}_2(x)=14[/tex]

By subtracting 4 from both the sides of the equation.

[tex]4\times \text{log}_2(x)=14-4[/tex]

Now divide the equation by 4

[tex]\text{log}_2(x)=\frac{10}{4}[/tex]

[tex]\text{log}_2(x)=2.5[/tex]

[If [tex]\text{log}_ab=x[/tex] , then [tex]b=a^{x}[/tex]]

[tex]x=(2)^{2.5}[/tex]

[tex]x = 5.657[/tex]

x ≈ 5.66

Therefore, Option C will be the correct option.

4+4•log2 x=14

x= 5.66

Answer:

50 miles

Step-by-step explanation:

hello,

let's note x the number of miles travelled heading west,

it takes 1 hour to travel 25 miles

so it takes x/25 hours to travel x miles

we know that in total it travels 7 hours so it will travel 7-x/25 hours heading North, then heading North it takes 1 hour to travel 19 miles

so in 7-x/25 hours it travels 19(7-x/25) miles

we can write, as the total distance is 145 miles

[tex]x+19(7-\dfrac{x}{25})=145\\<=> 25x+3325-19x=3625\\<=> 6x=300\\<=> x = 50[/tex]

we can verify

50 miles heading West takes 2 hours

in 5 hours it travels 19*5 = 95 miles

the total is 145 miles

so this is correct

hope this helps

Answer:

[tex]\boxed{\sf \ \ \ -\dfrac{15}{104} \ \ \ }[/tex]

Step-by-step explanation:

hello,

first of all let's assume that r is different from 0 as this is not allowed to divide by 0

[tex]\dfrac{1}{13r}=\dfrac{-8}{15}[/tex]

multiply by 13r it comes

[tex]\dfrac{13r}{13r}=1=\dfrac{-8*13r}{15}[/tex]

now multiply by 15

[tex]-8*13r=15\\<=> r = \dfrac{-15}{8*13}=-\dfrac{15}{104}[/tex]

hope this helps

Answer:[tex]r=-\frac{104}{15}[/tex] or -6.93333....

Step-by-step explanation:

[tex]\mathrm{Multiply\:both\:sides\:by\:}13[/tex]

[tex]13\cdot \frac{1}{13}r=13\left(-\frac{8}{15}\right)[/tex]    =-104/15

simplify

[tex]r=-\frac{104}{15}[/tex]

MARK BRAINLIEST PLEASE

Answer:

Hello, your answer is:

B. 3²×5

Step-by-step explanation:

Prime factorization of 45 is:

45 = 9 x 5

= 3²×5

Hope this helps you.. Good Luck

Answer:

B. 3² × 5

Step-by-step explanation:

45 can be written as a product of its prime factors.

45 = 3 × 3 × 5

45 = 3² × 5

Answer: NO, class limits and class marks are not meaningful to qualitative data.

Step-by-step explanation: Qualitative data are non-numerical data. They are collected mostly through observation. They include; sex, name and soon.

Class limits and class marks are groupings used in numerical data (quantitative data). They are not relevant and are meaningless to qualitative data classes as these data class are non- numerical.

Answer:

The height of the hill is 116.9 meters.

Step-by-step explanation:

The diagram depicting this problem is drawn and attached below.

From Triangle ABC

[tex]\tan 22^\circ=\dfrac{h}{150+x}\\\\h=\tan 22^\circ(150+x)[/tex]

From Triangle XBC

[tex]\tan 40^\circ =\dfrac{h}{x}\\\\h=x\tan 40^\circ[/tex]

Therefore:

[tex]h=\tan 22^\circ(150+x)=x\tan 40^\circ\\150\tan 22^\circ+x\tan 22^\circ=x\tan 40^\circ\\x\tan 40^\circ-x\tan 22^\circ=150\tan 22^\circ\\x(\tan 40^\circ-\tan 22^\circ)=150\tan 22^\circ\\x=\dfrac{150\tan 22^\circ}{\tan 40^\circ-\tan 22^\circ} \\\\x=139.30[/tex]

Therefore, the height of the hill

[tex]h=139.3\times \tan 40^\circ\\=116.9$ meters( correct to 1 d.p.)[/tex]

The height of the hill is 116.9 meters.

Answer:

The time period is 13 years.

Step-by-step explanation:

Interest rate (r )= 5% or 5%/12 = 0.42% per months

The investment amount (Present value) = $10500

Final expected amount (future value) = $20000

Since we have given the initial amount and final amount. Therefore we have to calculate the time period for which the initial amount is kept in the bank.

Use the below formula to find the time period.

Future value = present value (1 + r )^n

20000 = 10500(1+0.0042)^n

1.9047619 = (1+0.0042)^n

1.9047619 = 1.0042^n

n = 153.74 months.

Time in years = 153.74 / 12 = 12.8 years or 13 years (round off)

Answer:

[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]

Step-by-step explanation:

[tex]\frac{5x-11}{2x^2+x-6}[/tex]

Factor the denominator.

[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]

The fraction cannot be simplified further.

Answer:

solution,

[tex] \frac{5x - 11}{2 {x}^{2} + x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + (4 - 3)x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + 4x - 3x - 6 } \\ = \frac{5x - 11}{2x(x + 2) - 3(x + 2)} \\ = \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]

Hope this helps..

Answer:

Pair of compasses.

Step-by-step explanation:

These are used to inscribe circles/arcs.

Compasses are used in maths, navigation,e.t.c.

Hope it helps.

Answer:

x=2

Step-by-step explanation:

5(2x - 3) = 5

Divide by 5

5/5(2x - 3) = 5/5

2x-3 = 1

Add 3 to each side

2x-3 +3 = 1+3

2x = 4

Divide by 2

2x/2 = 4/2

x =2

Answer:

x = 2

Step-by-step explain:

5(2x-3) = 5

Divide both sides by 5

2x-3 = 1

Add 3 to both sides

2x = 4

Divide both sides by 2

x = 2

Answer:

116370.197$

Step-by-step explanation:

Jimmie invested $13,000 at 5.23% compounded monthly.

Jimmie's account balance (B) after 42 years:

B = principal x (1 + rate)^time

  = 13000 x (1 + (5.23/100)/12)^(42 x 12)

  = 116370.197$

Answer:

Yes. At the 0.05 significance level, there is enough evidence to support the claim that the proportion that support the candidate has significantly changed.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion that support the candidate has significantly changed.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]

The significance level is 0.05.

The sample 1, of size n1=800 has a proportion of p1=0.58.

[tex]p_1=X_1/n_1=460/800=0.58[/tex]

The sample 2, of size n2=1000 has a proportion of p2=0.52.

[tex]p_2=X_2/n_2=520/1000=0.52[/tex]

The difference between proportions is (p1-p2)=0.05.

[tex]p_d=p_1-p_2=0.58-0.52=0.05[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{464+520}{800+1000}=\dfrac{980}{1800}=0.54[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.54*0.46}{800}+\dfrac{0.54*0.46}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.00031+0.000248}=\sqrt{0.000558}=0.02[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.05-0}{0.02}=\dfrac{0.05}{0.02}=2.33[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]\text{P-value}=2\cdot P(z>2.33)=0.02[/tex]

As the P-value (0.02) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion that support the candidate has significantly changed.

Answer:124

Step-by-step explanation:

2x + 8 + x - 2 = 180

Add like terms

3x + 6 = 180

Subtract the 6 from both sides

3x + 6 - 6 = 180 - 6

3x = 174

Divide by 3

x = 58

Now we have to find the measure of angle ACD

2(58) + 8 = 124

Answer:

0.42

Process:

1 - 0.58

0.42

Answer:

873116133

Step-by-step explanation:

18576939 × 47

Multiply the numbers.

= 873116133

Answer: 873116133

Step-by-step explanation:

‘Hope this helps:)

Answer:

61% of the time a person will wait at least 1.872 seconds before the wave crashes in.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]

Uniform distribution from 0 to 4.8 seconds.

This means that [tex]a = 0, b = 4.8[/tex]

61% of the time a person will wait at least how long before the wave crashes in?

This is the 100 - 61 = 39% percentile, which is x for which [tex]P(X \leq x) = 0.39[/tex]. So

[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]

[tex]0.39 = \frac{x - 0}{4.8 - 0}[/tex]

[tex]x = 4.8*0.39[/tex]

[tex]x = 1.872[/tex]

61% of the time a person will wait at least 1.872 seconds before the wave crashes in.

Answer:

50%

Step-by-step explanation:

Even numbers on a 6-sided die are 2, 4, and 6.

3 numbers out of 6 are even.

3/6 = 1/2

0.5 = 50%

Answer:

  62.3538

Step-by-step explanation:

There is nothing to solve. If you need a decimal value, you can use a calculator or table of square roots.

Answer:

to determine the inverse of the given function, change f(x) to y, switch [tex]\boxed{x}[/tex] and y and solve for [tex]\boxed{y}[/tex]

The resulting function can be written as

[tex]f^{-1}(x)=x^2+\boxed{4}[/tex] where [tex]x\geq\boxed{0}[/tex]

Step-by-step explanation:

Hello,

f is defined for [tex]x\geq 4[/tex] as x-4 must be greater or equal to 0

and [tex]f(x)\geq 0[/tex]

so [tex]f^{-1}[/tex] is defined for [tex]x\geq 0[/tex]

and then we can write

[tex]x=(fof^{-1})(x)=f(f^{-1}(x))=\sqrt{f^{-1}(x)-4} \ so\\f^{-1}(x)-4=x^2 <=> f^{-1}(x)=x^2+4[/tex]

hope this helps

Answer:

a. The plane's speed in mph is 560

b. At this rate, the plane can travel 5,600 miles in 10 hours.

Step-by-step explanation:

In order to find the planes speed in mph, some simple arithmetic must be done and you should divide 3,360 by 6.   Now that you have determined that 3,360/6 equals 560, you know that in order to figure out how many miles the plane can travel in 10 hours, all you must do is multiply 560 by 10 which equals 5,600.

Answer:

Step-by-step explanation:

Hey there! :)

Answer:

x = 18 minutes.

Step-by-step explanation:

To solve this equation, set up a ratio.

# of towels over time taken:

[tex]\frac{6}{3} = \frac{36}{x}[/tex]

Cross multiply:

6x = 108

Divide both sides by 6:

6x/6 = 108/6

x = 18 minutes.

Answer:

In eighteen minutes she will have folded all 36