Tell whether the following two triangles can be proven congruent through SAS.

A.Yes, the two triangles are congruent because they’re both right triangles.
B.Yes, the two triangles are congruent because two sides and their included angle are congruent in both triangles.
C.No, the two triangles can only be proven congruent through SSS.
D.No, the two triangles can only be proven congruent through AAA.

Answer:

y= -6

Step-by-step explanation:

the y-intercept is -6, which corresponds to point (0,-6)

remember that you're using the

y=mx+b format of an equation of a line where b is the y-intercept.

Also, if you make x=0, y will be -6.

Answer:

Step-by-step explanation:

Answer:

The Sureset Concrete Company

The tons of gravel and sand that should be purchased each day are:

Sand = 800 tons

Gravel = 700 tons

Step-by-step explanation:

Two ingredients for producing concrete = sand and gravel

Cost of sand per ton = $6

Cost of gravel per ton = $8

Sand and gravel = 75% of the concrete

Therefore 25% (100 - 75%) will be made up of cement and water

Tons of concrete produced each day = 2,000

Sand and gravel = 1,500 (2,000 * 75%)

Sand <= 40% of 2,000 = 800 tons

Gravel => 30% of 2,000 = 700 (1,500 - 800) tons

To minimize costs,  800 tons of gravel and 700 tons of sand should be purchased each day.

Total cost incurred daily for both sand and gravel = $10,400 (800 * $6 + 700 * $8)

Answer:

x2 - 4x - 5 factored form is (x - 5)(x + 1)

Answer:

(x − 5)(x + 1)

Step-by-step explanation:

The answer above is correct.

Answer:

[tex]9x - 3 = 78 \\ 9x - 3 + 3 = 78 + 3 \\ 9x = 81 \\ \frac{9x}{9} = \frac{81}{9} \\ x = 9[/tex]

Answer:

[tex]9x - 3 = 78 \\9 x = 78 + 3 \\ 9x = 81 \\ x = \frac{81}{9} \\ x = 9[/tex]

Answer:

Net present value= $25.17

Step-by-step explanation:

We are told that The last dividend paid was $1.55 and that the dividend growth rate is constant at 1.5% for 2 years.

Thus;

1) After 1st year;

1.55 × (1 + 0.015) = 1.57325 Div1

After 2nd year;

1.57325 × (1 + 0.015) = 1.59685 Div2

After that 2 years it grows at 6% Constant rate forever;

1.59685 × (1 + 0.06) = 1.69266 Div3

Let's now use the dividend formula which grows in perpetuity at a rate of "g" since required return is 12%:

Thus;

V = 1.69266/(0.12 - 0.06) = 28.211

Thus; Div2 = 28.211 + 1.59685 ≈ 29.80785

Now, using the financial calculator of the Cash Flow function, we have:

Div0 = 0

Div1 = 1.57325

Div2 = 29.80785

i% = 12

Net present value = (1.57325/(1 + 0.12)) + ((1.59685 + 28.211)/(1 + 0.12)²)

Net present value= $25.17

Answer: 75%

Step-by-step explanation:

186.75/249 =.75

.75x100

75%

Answer:

f(n+1=-2f(n)

f(x)=-2f(n)

f(4)

f(4)=-2f(4)

Answer:

f(4) = - 1280

Step-by-step explanation:

Using the recursive rule and f(1) = 60 , then

f(2) = - 2f(1) = - 2 × 160 = - 320

f(3) = - 2f(2) = - 2 × - 320 = 640

f(4) = - 2f(3) = - 2 × 640 = - 1280

9514 1404 393

Answer:

  5/8

Step-by-step explanation:

The area of the smaller circles is proportional to the square of the ratio of their diameters. The two smallest circles have diameters equal to 1/4 the diameter of the largest circle. Hence their areas are (1/4)^2 = 1/16 of that of the largest circle.

Similarly, the medium circle has a diameter half that of the largest circle, so its area is (1/2)^2 = 1/4 of the are of the largest circle.

The smaller circles subtract 2×1/16 +1/4 = 3/8 of the area of the largest circle. Then the shading is 1-3/8 = 5/8 of the area of the largest circle.

Answer:

1 There is no number that make it divisible by 6 with no decimals

2 1,4,7

Step-by-step explanation:

2 23718/6= 3953

 23748/6= 3958

 23778/6= 3963

9514 1404 393

Answer:

  6

Step-by-step explanation:

Work backward.

If he has 24 after adding 6, he had 18 before that addition.

If he had 18 after tripling his collection, he had 18/3 = 6 cards to start with.

__

Note that this is the same process you would use if you started with an equation.

  3c +6 = 24 . . . . where c is the number of cards Johnny started with

  3c = 24 -6 = 18 . . . . . subtract 6 from the final number

  c = 18/3 = 6 . . . . . . . . divide the tripled value by 3 to see the original value

Johnny started with 6 cards.

Answer

14√5

Step-by-step explanation:

8√5 + 2√45

= 8√5 + 6√5

= 14√5

Hope this helps

Answer:

[tex]\boxed {\boxed {\sf 14 \sqrt{5}}}[/tex]

Step-by-step explanation:

We are asked to combine the radicals. We have the following expression:

[tex]8 \sqrt{5} + 2 \sqrt{45}[/tex]

Currently, we cannot combine these radicals. The value under the square root is not the same for both terms.

However, we can simplify the radical 2 √45 because the value under the radical is divisible by a perfect square.

45 can be divided by 9 (the perfect square) for a quotient of 5. So, we can simplify the radical using this information.

Break the radical into 2 radicals: 9 and 5.

[tex]8 \sqrt{5}+ 2 \sqrt{9}\sqrt{5}[/tex]

Notice that a perfect square is under the radical. √9 can be simplifed to 3.

[tex]8 \sqrt{5}+ 2 *3 \sqrt{5}[/tex]

Multiply 2 and 3.

[tex]8 \sqrt{3} + 6 \sqrt{5}[/tex]

Now the value under the radical is the same for both terms, and we can add the numbers in front of the radicals.

[tex]14 \sqrt{5}[/tex]

The radicals combined is equal to 14√5

Answer: the first part is 1.25. The second part is y=1.25x

Step-by-step explanation: edge 2021

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\text{19, 31, 15, 50, \& 20}[/tex]

[tex]\large\text{When you see or hear the word \underline{median}, think of the question}\\\large\text{asking you \bf what is the MIDDLE NUMBER.}\large\text{To find the}\\\large\text{middle number you have to put the numbers from descending}\\\large\text{(least/decreasing) or ascending (greatest/increasing) order}[/tex]

[tex]\large\text{15, 19, 20, 31, \& 20}[/tex]

[tex]\large\text{Make sure it is even on BOTH SIDES of the DATA SET}[/tex]

[tex]\large\text{It seems to be even on both sides of the number \bf 20}\large\text{ so \underline{20}}\\\large\text{can be your median/middle number in this given set}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: the median is \bf 20}}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]

9514 1404 393

Answer:

  x = 30 2/3

Step-by-step explanation:

Angles 4 and 5 are complementary, so we have ...

  m∠4 +m∠5 = 90°

  (2x +4) +(x -6) = 90

  3x -2 = 90 . . . . . . . . . collect terms

  3x = 92 . . . . . . . . . . add 2; next, divide by 3

  x = 92/3 = 30 2/3

Answer: [tex]24\ cm^2/s[/tex]

Step-by-step explanation:

Given

Each side of square is increasing at a rate of 4 cm/s

Side of a square when area is [tex]9\ cm^2[/tex]

Suppose a is side of the square

[tex]\Rightarrow a=\sqrt{9}\\\Rightarrow a=3\ cm[/tex]

Area is given by

[tex]\Rightarrow A=a^2\\\text{Differentiate area w.r.t time}\\\\\Rightarrow \dfrac{dA}{dt}=2a\dfrac{da}{dt}\\\\\Rightarrow \dfrac{dA}{dt}=2\times 3\times 4\\\\\Rightarrow \dfrac{dA}{dt}=24\ cm^2/s[/tex]

Area is increasing at a rate of [tex]24\ cm^2/s[/tex]

Answer:

24cm^2/ s

Step-by-step explanation:

Answer:

[tex]\sf \dfrac{1}{24}=0.0417=4.17\%\:\:(3\:s.f.)[/tex]

Step-by-step explanation:

Given information:

Contents of Jar 1:

Contents of Jar 2:

Probability Formula

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Therefore:

[tex]\sf P(white\:marble\:from\:Jar\:1)=\dfrac{4}{24}=\dfrac{1}{6}[/tex]

[tex]\sf P(white\:marble\:from\:Jar\:2)=\dfrac{20}{80}=\dfrac{1}{4}[/tex]

As the events are independent (i.e. drawing a marble from one jar does not influence or affect drawing a marble from the other jar), we can use the independent probability formula:

[tex]\sf P(A\:and\:B)=P(A) \cdot P(B)[/tex]

Therefore, the probability that a white marble will be drawn from both jars is:

[tex]\sf P(white\:marble\:from\:Jar\:1)\:and\:\sf P(white\:marble\:from\:Jar\:2)=\dfrac{1}{6} \cdot \dfrac{1}{4}=\dfrac{1}{24}[/tex]

#Jar 1

Total marbles =20+4=24

P(w)

#Jar 2

Total marbles=60+20=80

P(w)

P(w in total)

Answer:

a. 7 ÷ 4 yes

b. 4 ÷ 7 no

c. [tex]\frac{7}{4}[/tex] yes

d. [tex]\frac{4}{7}[/tex] no

e. 7 × [tex]\frac{1}{4}[/tex] yes

f. [tex]1\frac{3}{4}[/tex] yes

Step-by-step explanation:

hope this helps ^^

Answer:

3/2 x^5 y

Step-by-step explanation:

3x^5y^3

----------------

2y^2

Simplify the y terms

y^3 / y^2 = y^(3-2) = y

3/2 x^5 y

Answer:

[tex] \frac{3}{2} x {}^{5} y {}^{} [/tex]

Step-by-step explanation:

it's all in the image

Answer:

Hence the value of p is 0.04746.

Step-by-step explanation:

The test statistic is

[tex]Z=(\bar x-\mu)/(s/vn)\\\\=(355-390)/(115/ \sqrt(30))\\\\=-1.667[/tex]

The p-value= P(Z<-1.67) =0.04746. (from standard distribution table)

Therefore p-value =0.04746.

Answer:

128 mph

Step-by-step explanation:

1 hour = 400

4 hours = 240

240+400= 640

4+1 = 5

640/5=128

Answer:

2.167 (rounded to the nearest hundredths).

Step-by-step explanation:

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

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, divide 2 from both sides of the equation:

(2(3x - 4))/2 = (5)/2

3x - 4 = 2.5

Next, isolate the variable, x. Add 4 to both sides of the equation:

3x - 4 (+4) = 2.5 (+4)

3x = 2.5 + 4

3x = 6.5

Then, divide 3 from both sides of the equation:

(3x)/3 = (6.5)/3

x = 6.5/3 = 2.167 (rounded).

~

Answer:

We have this equation

2*(3x-4) = 5

We can start solving the parentheses

2*(3x- 4) = 5

6x - 8 = 5

We can add 8 to both sides

6x - 8 + 8 = 5 + 8

6x = 13

And divide by 6

6x/6 = 13/6

x = 13/6

Answer:

37

Step-by-step explanation:

7 + (5×6)

= 7 + 30

= 37

.................

Answer:

37

Step-by-step explanation:

First Step: Multiply

5x6=30

Second Step: Add

30+7=37

Therefore your answer is 37

Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?  

Answer:

0.6836

Step-by-step explanation:

(weight - mean weight) = 48

Variance, s² = 204,304

Sample size, n = 89

We need to obtain the Zscore :

Zscore = (X - mean) / standard Error

Zscore = (weight - mean weight ) / (s/√n)

s = √204304 = 452

The difference from the meanncoukdnbe either to the right or left :

Zscore = - 48 / (452/√89) OR 48 / (452/√89)

Zscore = - 48 / 47.911904 OR - 48 / 47.911904

Zscore = - 1.002 or 1.002

P(Z < - 1.002) = 0.1582 (using Z table)

P(Z < 1.002) = 0.8418

P(Z < 1.002) - P(Z < - 1.002)

0.8418 - 0.1582

= 0.6836

Answer:

It will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.

Step-by-step explanation:

We can write a half-life function to model our function.

A half-life function has the form:

[tex]\displaystyle A=A_0\left(\frac{1}{2}\right)^{t/d}[/tex]

Where A₀ is the initial amount, t is the time that has passes (in this case seconds), d is the half-life, and A is the amount after t seconds.

Since the half-life of the element is 30 seconds, d = 30. Our initial sample has nine grams, so A₀ is 9. Substitute:

[tex]\displaystyle A=9\left(\frac{1}{2}\right)^{t/30}[/tex]

We want to find the time it will take for the element to decay to 0.72 grams. So, we can let A = 0.72 and solve for t:

[tex]\displaystyle 0.72=9\left(\frac{1}{2}\right)^{t/30}[/tex]

Divide both sides by 9:

[tex]\displaystyle 0.08=\left(\frac{1}{2}\right)^{t/30}[/tex]

We can take the natural log of both sides:

[tex]\displaystyle \ln(0.08)=\ln\left(\left(\frac{1}{2}\right)^{t/30}\right)[/tex]

By logarithm properties:

[tex]\displaystyle \ln(0.08)=\frac{t}{30}\ln(0.5)[/tex]

Solve for t:

[tex]\displaystyle t=\frac{30\ln(0.08)}{\ln(0.5)}\approx109.3\text{ seconds}[/tex]

So, it will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.

Answer:

The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

Of 1000 randomly selected cases of lung cancer, 450 resulted in death within 5 years.

This means that [tex]n = 1000, \pi = \frac{450}{1000} = 0.45[/tex]

96% confidence level

So [tex]\alpha = 0.04[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.04}{2} = 0.98[/tex], so [tex]Z = 2.054[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 - 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4177[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 + 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4823[/tex]

The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).

Answer:

19 beers must be sampled.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees.

This means that [tex]\sigma = 0.26[/tex]

If we want to be 90% confident that the sample mean beer temperature is within 0.1 degrees of the true mean temperature, how many beers must we sample?

This is n for which M = 0.1. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.1 = 1.645\frac{0.26}{\sqrt{n}}[/tex]

[tex]0.1\sqrt{n} = 1.645*0.26[/tex]

[tex]\sqrt{n} = \frac{1.645*0.26}{0.1}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.645*0.26}{0.1})^2[/tex]

[tex]n = 18.3[/tex]

Rounding up:

19 beers must be sampled.

Answer:

H0 : μN ≤ μD

H1 : μN > μD

Right tailed

Test statistic = 1.33

Pvalue = 0.097

Fail to reject the Null

Step-by-step explanation:

H0 : μN ≤ μD

H1 : μN > μD

The test is right tailed ; culled from the direction of the greater than sign ">"

Night students :

n1 =30 x1= 3.34 s1 = 0.02

Day students:

n2 = 30 x2 = 3.32 s2 = 0.08

The test statistic :

(x1 - x2) / √(s1²/n1) + (s2²/n2)

T= (3.34 - 3.32) / √(0.02²/30) + (0.08²/30)

T = 0.02 / 0.0150554

Test statistic = 1.328

Using the conservative approach ;

df = Smaller of n1 - 1 or n2 - 1

df = 30 - 1 = 29

Pvalue(1.328, 29) = 0.097

At α = 0.10

Pvalue < α ; Hence, we reject H0 ; and conclude that there is significant evidence that GPA of night student is greater than GPA of day student

Answer:

b=2

Step-by-step explanation:

Answer:

i dont knowwww dhehje ejhdjeke jsienje

Answer:

8cm and 9 cm​

Step-by-step explanation:

Sum of sides rule:

The sum of the two smallest sides of a triangle has to be greater than the third side.

5 cm and 8 cm

One side is 5, other 8, 5 + 8 = 13. The sum has to be greater than 13, so this is not possible.

6cm and 7 cm

6 + 7 = 13, same as above, not possible.

7cm and 2 cm

7 + 2 = 9 < 13, so not possible.

8cm and 9 cm​

8 + 9 = 17 > 13, so possible, and this is the answer.