Multiply (2.0 ⋅ 10−4) ⋅ (3.1 ⋅ 10−20). Express the answer in scientific notation. 6.2 ⋅ 10−80 6.2 ⋅ 10−24 6.2 ⋅ 1024 6.2 ⋅ 1080

Answer: 54 mL

Step-by-step explanation:

Simply do 9(number of containers)*6(Syrup per container) to get 54 mL of syrup.

Hope it helps <3

Answer:

 [tex]x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right][/tex]

Step-by-step explanation:

According to the given situation, The computation of all x in a set of a real number is shown below:

First we have to determine the [tex]\bar x[/tex] so that [tex]A \bar x = 0[/tex]

[tex]\left[\begin{array}{cccc}1&-3&5&-5\\0&1&-3&5\\2&-4&4&-4\end{array}\right][/tex]

Now the augmented matrix is

[tex]\left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\2&-4&4&-4\ |\ 0\end{array}\right][/tex]

After this, we decrease this to reduce the formation of the row echelon

[tex]R_3 = R_3 -2R_1 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&2&-6&6\ |\ 0\end{array}\right][/tex]

[tex]R_3 = R_3 -2R_2 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right][/tex]

[tex]R_2 = 4R_2 +5R_3 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&4&-12&0\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right][/tex]

[tex]R_2 = \frac{R_2}{4}, R_3 = \frac{R_3}{-4} \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&1\ |\ 0\end{array}\right][/tex]

[tex]R_1 = R_1 +3 R_2 \rightarrow \left[\begin{array}{cccc}1&0&-4&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right][/tex]

[tex]R_1 = R_1 +5 R_3 \rightarrow \left[\begin{array}{cccc}1&0&-4&0\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right][/tex]

[tex]= x_1 - 4x_3 = 0\\\\x_1 = 4x_3\\\\x_2 - 3x_3 = 0\\\\ x_2 = 3x_3\\\\x_4 = 0[/tex]

[tex]x = \left[\begin{array}{c}4x_3&3x_3&x_3\\0\end{array}\right] \\\\ x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right][/tex]

By applying the above matrix, we can easily reach an answer

Answer:

25 and 30

Step-by-step explanation:

Let the smaller consecutive multiples of 5 be x. Therefore, other consecutive multiples will be x + 5.

Now as per statement the sum of two consecutive multiples of 5 is 55. To find the multiples. Thus

x + x + 5 = 55

2x + 5 = 55

2x = 55 - 5

2x = 50

x = 50/2

x = 25

This the smaller consecutive multiples of 5 is 25, the other consecutuve multiple is x+ 5, 25 + 5 = 30.

The consecutive multiple numbers of 5 are 25 and 30

Answer the two consecutive multiples of 5 are 25 and 30

Answer:

25 and 30.

Step-by-step explanation:

Let the smaller consecutive multiple of 5 be 'x'. So, the other multiple will be x + 5.

Now, the statement is the sum of two consecutive multiples of 5 is 55. To find the multiples, we must simplify as below.

x + x + 5 = 55

2x + 5 = 55

2x = 55 - 5

2x = 50

x = 50/2

x = 25

We observe that the smaller consecutive is 25, so the other multiple is x+ 5, 25 + 5 = 30.

(Hope this helps and please mark as the brainliest)

Answer: 4 miles

Step-by-step explanation:

If Ashley ran 1 mile 4 times, she ran 1+1+1+1, or 1*4, or 4 miles.

Hope it helps <3

Answer:

x>3

Step-by-step explanation:

Answer:

x = 64

Step-by-step explanation:

A circle equal 360 degrees

180 + 90 + x + 26 = 360

Combine like terms

296+x = 360

Subtract 296 from each side

296+x-296 = 360-296

x = 64

Answer:

x = [tex]\frac{3}{4}(n-1)[/tex]

Step-by-step explanation:

It's given in the question that '' The number is 75% of one less than a number n"

Let the number is 'x'.

One less than a number 'n' will be = (n - 1)

75% of one less than a number will be = 75% of (n -1)

                                                                = [tex]\frac{75}{100}(n-1)[/tex]

                                                                = [tex]\frac{3}{4}(n-1)[/tex]

Therefore, the desired expression to get the number 'x' will be,

x = [tex]\frac{3}{4}(n-1)[/tex]

Answer:

3/4(n-1)

Step-by-step explanation:

did it in rsm

Working backwards, on Wednesday morning we have 60 / (1/2) = 120 pounds of ice.

2/3 melts on Tuesday so 120 pounds must be 1/3 of the ice.

120 / (1/3) = 360

Answer: D. 360

Answer:

Step-by-step explanation:

t1=2

t2=-8

r=t2/t1=-8/2=-4

t10=t1*r⁹

t10=2*(-4)⁹= -2*(2²)⁹

t10= -2¹⁹= -524288

Answer:

-524288

Step by step

so use the formula

ar^n-1

so

a is first term

r is common ratio

n is number of terms

so

get r which is -8/2=-4

then apply

2×(-4^9)=answer

not sure

Complete question:

If x = –3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

a) The discriminant is negative.

b) The discriminant is –3.

c) The discriminant is 0.

d) The discriminant is positive.

Answer:

c) The discriminant is 0.

Step-by-step explanation:

Here, x = -3 is the only x intercept of graph of a quadrant equation.

In this case the determinant of the quadrant equation will be 0.

i.e, x = 0

The determinant of the quadrant equation will be zero because, since x = -3 is the only x intercept of the graph, the quadrant equation will have equal roots. Also, when there are equal roots in a quadrant equation, the discriminant tends to zero.

Therefore the correct answer is (c) The discriminant is 0.

D = 0

Answer:

C

Step-by-step explanation:

taking the quiz rn

Answer:

The answer is below

Step-by-step explanation:

The corresponding data are missing, which are the following:

Strikes (pre):

29

32

44

34

19

Strikes (post):

51

45

68

92

64

We have to say the difference between the post-pre values of the strike. The d will be the average of the differences between the post and pre values. If Kara is to show improvement, her post-workout attacks should be more than the pre-workout values. Let m be the population mean of the difference:

H0: m = 0 the mean difference in Strikes between post and pre is zero.

H0: m>0, the mean difference in strikes between post and pre is more than zero.

Answer:

86.9

Step-by-step explanation:

Find the number in the tenth place 9 and look one place to the right for the rounding digit 4 Round up if this number is greater than or equal to 5 and round down if it is less than 5

Hope this can help

Answer:

If we have two functions g(x) and f(x)

I suppose that the functions here are:

f(x) = 2 - √(4*x)

g(x) = -3*x

First, let's analyze the functions:

g(x) as not any problem for any value of x, so the domain is the set of all the real numbers.

f(x) has a square root on it, and we know that the square root of a negative number is equal to a complex number, so here we can not have negative values of x.

The domain of f is D = x ∈ {0, ∞}

Then (gof)(x) = g(f(x)) = -3*(2 - √(4*x)) = -6 + 3*√(4*x)

We can see that g(x) does not have any problem, and the problems with f(x) remain there, so the domain of the composition is equal to the domain of f(x):

D =  x ∈ {0, ∞}

Answer:

(i) 520

(ii) 2

Step-by-step explanation:

(i) x³ + y³

Plug x as 2, and y as 8.

(2)³ + (8)³

Solve for exponents.

8 + 512

Add.

= 520

(ii) ∛y

Plug y as 8.

∛(8)

Solve for cube root.

= 2

Answer:

( i ) 520

( ii ) 2

Step-by-step explanation:

We can find this solution by plugging in known values -

If x = 2, y = 8

x³+y³ = ( 2 )³ + ( 8 )³ = 8 + 512

= 520

Know let us move on to the second half -

We only need one part of this information now, y = 8. If so,

∛y = ∛8

2 x 2 x 2 = 8 - and thus 2 should be our solution for this portion.

Answer: Monomial.

Step-by-step explanation:

Ok, when we have a polynomial with only one term, this is a monomial.

If the polynomial has two terms, this is a binomial.

If the polynomial has 3 terms, this is a trinomial.

And so on.

In this particular case we have:

52*c^2*y^4

Where c and y may be variables.

We can see that here we have only one term, so this would be a monomial.

(notice that the number of variables does not affect the type of polynomial in this case, only the number of terms)

Answer:

binomial.

Step-by-step explanation:

The polynomial −50c3z3−41y220z4 has 2 terms, so it is a binomial.

It would have to have a positive slope and the bottom needs to be shaded, since -2y is negative it means we will be dividing by a negative. The inequality sign will switch.

also if it is < then the line is dotted, if it’s the “greater or equal to sign” then the line is not dotted.

dunno if I explained it very well

The shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

Given is the inequality as -

x - 2y² < 12

The given inequality is -

x - 2y² < 12

2y² - x < - 12

2y² < x - 12

y² < (x/2) - 6

[tex]$y < \pm\sqrt{\frac{x}{2}-6 }[/tex]

[tex]$y < \sqrt{\frac{x}{2}-6 }[/tex]        

and

[tex]$y < -\sqrt{\frac{x}{2}-6 }[/tex]

Refer to the graph of the equation attached. The shaded region common to both the inequalities represents the solution set of the inequality.

Therefore, the shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.

To solve more questions on inequality, visit the link-

https://brainly.com/question/11897796

#SPJ7

Answer:

The null hypothesis is ;

H0 ≥ 12

While the alternative hypothesis H1 is ;

H1 < 12

Step-by-step explanation:

Here, we want to correctly identify the null hypothesis H0 and the alternative hypothesis H1

The null hypothesis is as follows ;

H0 ≥ 12

While the alternative hypothesis H1 is ;

H1 < 12

Answer:

4.87

Step-by-step explanation:

According to the given situation, for calculation of standard deviation for the number of people first we need to calculate the variance which is shown below:-

Variance is

[tex]np(1 - p)\\\\ = 500\times (0.05)\times (1 - 0.05)[/tex]

After solving the above equation we will get

= 23.75

Now the standard deviation is

[tex]= \sqrt{\sigma} \\\\ = \sqrt{23.75}[/tex]

= 4.873397172

or

= 4.87

Therefore for computing the standard variation we simply applied the above formula.

Answer: 25 square units

Step-by-step explanation:

We mark the points, A(2,0), B(7,0), C(10,3), D (5,3). on a graph and then joined them to make parallelogram ABCD as provided in the attachment.

Area of parallelogram  = Base x corresponding height

From the figure, base AB = 7 - 2 units = 5 units

corresponding height: h= 5 units

Now , Area of parallelogram  ABCD = base AB x corresponding height

= 5 x 5 square units

= 25 square units

Hence,  the area of parallelogram  ABCD is 25 square units .

approximately 36.633 cm if you use pi = 3.14

approximately 36.6519 cm if you use the calculator's stored value of pi

Work Shown:

L = arc length, r = radius, x = central angle in degrees

L = (x/360)*2*pi*r

L = (300/360)*2*pi*7

L = (35/3)pi .... exact arc length in terms of pi

L = (35/3)*3.14

L = 36.633 .... approximate arc length

Keep in mind that I used pi = 3.14 which isn't that great an approximation for pi. If you want to use more digits of pi, then use your calculator's built in version of it to get (35/3)*pi = 36.6519; of course it will depend on which option your teacher prefers.

Answer:

The infinite series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} \frac{8/k}{\sqrt{k + 7}}[/tex] indeed converges.

Step-by-step explanation:

The limit comparison test for infinite series of positive terms compares the convergence of an infinite sequence (where all terms are greater than zero) to that of a similar-looking and better-known sequence (for example, a power series.)

For example, assume that it is known whether [tex]\displaystyle \sum\limits_{k = 1}^{\infty} b_k[/tex] converges or not. Compute the following limit to study whether [tex]\displaystyle \sum\limits_{k = 1}^{\infty} a_k[/tex] converges:

[tex]\displaystyle \lim\limits_{k \to \infty} \frac{a_k}{b_k}\; \begin{tabular}{l}\\ $\leftarrow$ Series whose convergence is known\end{tabular}[/tex].

Let [tex]a_k[/tex] denote each term of this infinite Rewrite the infinite sequence in this question:

[tex]\begin{aligned}a_k &= \frac{8/k}{\sqrt{k + 7}}\\ &= \frac{8}{k\cdot \sqrt{k + 7}} = \frac{8}{\sqrt{k^2\, (k + 7)}} = \frac{8}{\sqrt{k^3 + 7\, k^2}} \end{aligned}[/tex].

Compare that to the power series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} b_k[/tex] where [tex]\displaystyle b_k = \frac{1}{\sqrt{k^3}} = \frac{1}{k^{3/2}} = k^{-3/2}[/tex]. Note that this

Verify that all terms of [tex]a_k[/tex] are indeed greater than zero. Apply the limit comparison test:

[tex]\begin{aligned}& \lim\limits_{k \to \infty} \frac{a_k}{b_k}\; \begin{tabular}{l}\\ $\leftarrow$ Series whose convergence is known\end{tabular}\\ &= \lim\limits_{k \to \infty} \frac{\displaystyle \frac{8}{\sqrt{k^3 + 7\, k^2}}}{\displaystyle \frac{1}{{\sqrt{k^3}}}}\\ &= 8\left(\lim\limits_{k \to \infty} \sqrt{\frac{k^3}{k^3 + 7\, k^2}}\right) = 8\left(\lim\limits_{k \to \infty} \sqrt{\frac{1}{\displaystyle 1 + (7/k)}}\right)\end{aligned}[/tex].

Note, that both the square root function and fractions are continuous over all real numbers. Therefore, it is possible to move the limit inside these two functions. That is:

[tex]\begin{aligned}& \lim\limits_{k \to \infty} \frac{a_k}{b_k}\\ &= \cdots \\ &= 8\left(\lim\limits_{k \to \infty} \sqrt{\frac{1}{\displaystyle 1 + (7/k)}}\right)\\ &= 8\left(\sqrt{\frac{1}{\displaystyle 1 + \lim\limits_{k \to \infty} (7/k)}}\right) \\ &= 8\left(\sqrt{\frac{1}{1 + 0}}\right) \\ &= 8 \end{aligned}[/tex].

Because the limit of this ratio is a finite positive number, it can be concluded that the convergence of [tex]\displaystyle a_k &= \frac{8/k}{\sqrt{k + 7}}[/tex] and [tex]\displaystyle b_k = \frac{1}{\sqrt{k^3}}[/tex] are the same. Because the power series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} b_k[/tex] converges, (by the limit comparison test) the infinite series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} a_k[/tex] should also converge.

Answer:

x = 80

y = 130

Step-by-step explanation:

The 2 angles are supplementary. so, x-30 + x+50 = 180.

We solve and get 2x = 180-20

x = 80

y = x+50, because of parallel rules.

y = 130

Answer:

x = 80

y = 130

Step-by-step explanation:edge 2020

The correct graph will be the first one (A)

Answer:

x=3 or/and x= -7/3

Step-by-step explanation:

+1= +1

3x = 9

9 divided by 3 is x= 3

+1= +1

3x = -7

-7 divided by 3 is x= -7/3

Answer:

[tex]\huge\boxed{x=3\ \vee\ x=-\dfrac{7}{3}}[/tex]

Step-by-step explanation:

[tex]|a|=\left\{\begin{array}{ccc}a&\text{for}\ a\geq0\\-a&\text{for}\ a<0\end{array}\right\\\\|a|=k\to a=k\ \vee\ a=-k\ \text{for}\ k>0\\==========================\\\\|3x-1|=8\iff3x-1=8\ \vee\ 3x-1=-8\\\\\begin{array}{cccc}3x-1=8&\vee&3x-1=-8&\text{add 1 to both sides}\\3x-1+1=8+1&\vee&3x-1+1=-8+1\\3x=9&\vee&3x=-7&\text{divide both sides by 3}\\\dfrac{3x}{3}=\dfrac{9}{3}&\vee&\dfrac{3x}{3}=\dfrac{-7}{3}\\x=3&\vee&x=-\dfrac{7}{3}\\\end{array}[/tex]

Answer:

The new extra processor would take 20 hours to download the movie.

Step-by-step explanation:

This word problem presents two variables: [tex]n[/tex] - Processing capacity, dimensionless; [tex]t[/tex] - Download time, measured in hours. Both variables exhibit a relationship of inverse proportionality, that is:

[tex]t \propto \frac{1}{n}[/tex]

[tex]t = \frac{k}{n}[/tex]

Where [tex]k[/tex] is the proportionality constant.

Now, let suppose that original processor has a capacity of 1 ([tex]n = 1[/tex]), the proportionality constant is: ([tex]t = 5\,h[/tex])

[tex]k = n\cdot t[/tex]

[tex]k = (1)\cdot (5\,h)[/tex]

[tex]k = 5\,h[/tex]

The equation is [tex]t = \frac{5}{n}[/tex] and if time is reduced to 4 hours by adding an extra processor, the processing capacity associated with this operation is: ([tex]t = 4\,h[/tex])

[tex]n = \frac{5}{t}[/tex]

[tex]n = \frac{5\,h}{4\,h}[/tex]

[tex]n = 1.25[/tex]

Then, the extra processor has a capacity of 0.25. The time required for the new extra processor to download the movie is: ([tex]n = 0.25[/tex])

[tex]t = \frac{5\,h}{0.25}[/tex]

[tex]t = 20\,h[/tex]

The new extra processor would take 20 hours to download the movie.

Answer:

Side a^2 = 49 + 16

Side a^2 = 65

Side a = 8.062

sin (B) = 4 / 8.062

cos (B) = 7 / 8.062

tan (B) = 4 / 7

cot (B) = 7 / 4

sec (B) = 8.062 / 7

csc (B) = 8.062 / 4

Step-by-step explanation:

Answer:

csc B = 13/12

Step-by-step explanation:

csc B = 1 / sin B

The sin B is

sin B = opp/ hyp  so

csc B = hyp /opp

csc B = 26 / 24

csc B = 13/12

Answer:

13/12

Step-by-step explanation:

sin θ = opposite/ hypotenuse

csc θ = 1/sinθ

csc θ  = hypotenuse/opposite

csc (B)  = 26/24

csc (B)  = 13/12

Answer:

The geometric mean of the measures of the line segments AD and DC is  60/13

Step-by-step explanation:

Geometric mean: BD² = AD×DC

BD = √(AD×DC)

hypotenuse/leg = leg/part

ΔADB: AC/12 = 12/AD

AC×AD = 12×12 = 144

AD = 144/AC

ΔBDC: AC/5 = 5/DC

AC×DC = 5×5 = 25

DC = 25/AC

BD = √[(144/AC)(25/AC)]

BD = (12×5)/AC

BD= 60/AC

Apply Pythagoras theorem in ΔABC

AC² = 12² + 5²

AC² = 144+ 25 = 169

AC = √169 = 13

BD = 60/13

The geometric mean of the measures of the line segments AD and DC is BD = 60/13

Answer:

[tex]cos57 = 0.5446[/tex]

[tex]sin57 = 0.8387[/tex]

[tex]tan57 = 1.5399[/tex]

Step-by-step explanation:

Given

[tex]cos 94\° cos 37\° + sin 94\° sin 37\°[/tex]

Required

Determine the

- sin

- cosine

- tangent

of an angle

The given expression can be represented as follows;

[tex]cosAcosB + sinAsinB[/tex]

Where A = 94 and B = 37

In trigonometry:

[tex]cosAcosB + sinAsinB = cos(A - B)[/tex]

Substitute 94 for A and 37 for B

[tex]cos(A - B) = cos(94 - 37)[/tex]

[tex]cos(A - B) = cos(57)[/tex]

Hence, the angle is 57;

Since 57 is not a special angle; I'll solve using a calculator

[tex]cos57 = 0.5446[/tex]

[tex]sin57 = 0.8387[/tex]

[tex]tan57 = 1.5399[/tex]