By rounding to 1 significant figure, estimate the answers to these questions:
a) 687 × 164
b) 476 × 2354
c) 8612 × 1497

Answer:

Step-by-step explanation:

15 vowels plus 25 consonants is 40

so 15/40 then you take the one vowel out and there is 39 so then it is 14 over 39.

Answer:

a. [tex]y = -(x+1)^2+4[/tex]

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

Step-by-step explanation:

a. Vertex is (-1, 4)

so you get

[tex]y = a(x+1)^2+4[/tex]

plug in (1, 0) and get the a value

[tex]0 = a(1+1)^2+4\\0 = a*2^2 + 4\\0 = 4a + 4\\-4 = 4a\\a = -1[/tex]

final eq:

[tex]y = -(x+1)^2+4[/tex]

b. Vertex is (2, -3)

so you get

[tex]y = a(x-2)^2-3[/tex]

plug in (0, -1) and get the a value

[tex]-1 = a(0-2)^2-3\\-1 = a*(-2)^2 -3\\-1 = 4a -3\\2 = 4a\\a = \frac{1}{2}[/tex]

final eq:

[tex]y = \frac{1}{2} (x-2)^2-3[/tex]

Answer:

1/2 divided by 1/4

Step-by-step explanation:

so 2

hope this helps :)

Answer: 77 dollars

Step-by-step explanation:

6 sheets  = 33 dollars

14 sheets = {(33/6)*14} = 77 dollars

Answer:

Approximately 1.77

To solve it I used a scientific calculator

Answer:The square root of Pi is approximately 1.77245.

Step-by-step explanation:

i hope i got it rigth ....

Factoring is an important process that helps us understand more about our equations. Through factoring, we rewrite our polynomials in a simpler form, and when we apply the principles of factoring to equations, we yield a lot of useful information. There are a lot of different factoring techniques.

Answer:-1 and 3

Step-by-step explanation:

Took it on edge :)

The required solution of the given equation is (3, -1) which is the correct option (C).

The quadratic function is defined as a function containing the highest power of a variable is two.

The equation is below represented by the system shown here.

2x² - 3x - 2 = x + 4

Rearrange the terms of variables and constants in the above equation

2x² - 3x - 2 - x - 4 = 0

Apply the arithmetic operation in the likewise terms,

2x² - 4x - 6 = 0

2x² - 6x + 2x - 6 = 0

2x(x - 3) + 2(x - 3) = 0

(x - 3)(2x + 2) = 0

(x - 3) = 0 and (2x + 2) = 0

x = 3 and 2x = - 2

x = 3 and x = - 1

Therefore, the required solution of the given equation is (3, -1).

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Answer: $33.89

Step-by-step explanation:

$59.87 - $25.98 = $33.89

Answer:

33.89

Step-by-step explanat33.89ion:

$59.87-$25.98

Answer:

B 9 cups

Step-by-step explanation:

Grape juice to orange juice ratio is 2:3, for every 2 cups of grape juice 3 cups of orange juice are used.

6/2=3

3 x 3 =9

for every 6 cups of grape juice, 9 cups of orange juice are used

Check for answer by seeing if the ratio matches up.

6:9 simplified is 2:3.

Answer is correct.

Answer:

6

Step-by-step explanation:

[tex]-\frac84 divided-\frac39\\-2 divided- \frac13\\-2 \cdot -3\\6[/tex]

Answer:

27 in each row

Step-by-step explanation:

216/8=27

Answer:

27 Apple Trees in each row

Step-by-step explanation:

216 divided by 8 gives us 27

The equation is 216/8=27

Answer:

All angles and opposite angle are equal;opposite sides are parallel.

Step-by-step explanation:

Answer:

they both have 4 sides and they both have paralell sides.

Step-by-step explanation:

The Lounge suite price in total is, $2648.

Given that, $2,000 lounge suite was sold under a hire contract. A deposit of $200 was made. The balance and interest were then paid off in equal monthly instalment of $68 over three years.

Under a rent purchase agreement, a purchaser pays an initial deposit and takes the item away. The purchaser  makes regular repayments (instalments). The instalments embrace each repayment of the debt and also the interest being charged by the seller. At the top of the amount of the agreement, the purchaser owns the item.

As mentioned, the lounge suite was purchased by paying $200 deposit and also the rest quantity through instalments i.e $68 over three years.

The total price of the lounge suite are going to be,

total price = deposit amount + instalments

               = $200 +  $68 over 3years

               = $200 + $68 (3* 12)            ( since, annually has twelve months)

                =$200 + $68(36)

                =$200 + $2448

                =$2648

Therefore the overall price of the lounge suite is, $2648.

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Answer:

C Step 3

Step-by-step explanation:

Answer:

C: Step 3 is where the mistake was made

Step-by-step explanation:

The annual interest rate before compounding will be 7.0404%.

What is compound interest ?

Compound interest is the type of interest that is calculated using both the principal and the interest that has accumulated over the preceding period.

Given that Bank D pays 7.289% annual yield on an investment account in which interest is compound weekly.

We know that there are 52 weeks in 1 normal year.

The annual interest rate before compounding can be calculated using the formula of compound interest.

Compound interest = Amount - Principal

And Amount is given by the formula ;

Amount = P × [tex](1 +R)^n[/tex]

where ; R is in %.

Let's assume P = $1.

So , the compound interest will be equal to

CI =  P × [tex](1 +R)^n[/tex] - P

CI + P = P × [tex](1 +R)^n[/tex]

CI + 1 = 1 × [tex](1 + R)^n[/tex]

As the investment account is compound weekly, so the annual interest rate will be divide by 52 or it will be R / 52.

1 + (7.289/100) = 1 + (R/52)^52

0.07289 = (R/52)^52

Solving this we will get ;

R = 0.0704035593

or

R = 7.0404%

Therefore , the annual interest rate before compounding will be 7.0404%.

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Answer:

A. (X =4) is the event that the student has four cousins: P(X-4) is the probability of the event that the student has four cousins.

Step-by-step explanation:

An event is an individual outcome or any number of outcomes of a random experiment or trial. An even that contains only one sample point is called a simple event. A compound event contains more than 1 sample point and is formed by the union of simple points.

An event A is said to occur only and if only the outcome of the experiment corresponds to some element of A.

In the given question the first symbolic representation gives an event and the second symbolic representation gives the probability.

The probability of X = 2 or 4 is given by P (X=2) or  P (X=4) symbollically.

So A is the best choice.

The relative frequency gives the probability  so choice B,C and D are wrong.

Answer:

There will be 25 grams left after 2 days.

Step-by-step explanation:

Half-life describes the amount of time it takes for a cell to turn from one condition to another.

To find the amount of grams for the second day, divide 100 by 2.

100 ÷ 2 = 50

Now, to find the amount of grams for the third day, we need to divide 50 by 2.

50 ÷ 2 = 25

Therefore, there will be 25 grams left after 2 days.

Hope this helps! :D

First, we observe that

[tex]4x-x^2 = x(4-x) = 0 \implies x=0 \text{ or } x = 4[/tex]

and

[tex]4x-x^2 = 4-(x-2)^2 \le 4[/tex]

so that [tex]R[/tex] is in the first quadrant. Any line [tex]y=mx[/tex] that slices this region into two pieces must then have a slope between [tex]m=0[/tex] and [tex]m=4[/tex] (which is the slope of the tangent line to the curve through the origin).

The parabola and line meet at the origin, and again when

[tex]4x - x^2 = mx \\\\ ~~~~ \implies x^2 + (m-4)x = x (x + m - 4) = 0 \\\\ ~~~~\implies x = 4-m[/tex]

with [tex]4x-x^2\ge mx[/tex] for [tex]0\le x\le4-m[/tex].

Now, the total area of [tex]R[/tex] is

[tex]\displaystyle \int_0^4 (4x-x^2) \, dx = \left(2x^2 - \frac{x^3}3\right)\bigg|_0^4 = \frac{32}3[/tex]

so that half the area is 16/3.

The area of the left piece (containing the origin) is

[tex]\displaystyle \int_0^{4-m} ((4x-x^2) - mx) \, dx = \left(\frac{4-m}2 x^2- \frac{x^3}3\right)\bigg|_0^{4-m} = \frac{(4-m)^3}6[/tex]

Solve for [tex]m[/tex].

[tex]\dfrac{(4-m)^3}6 = \dfrac{16}3[/tex]

[tex](4-m)^3 = 32[/tex]

[tex]4 - m = \sqrt[3]{32} = 2\sqrt[3]{4}[/tex]

[tex]\boxed{m = 4 - 2\sqrt[3]{4} \approx 0.825}[/tex]

Answer:

you need to prove AB=AD

Step-by-step explanation:

Answer:

The selling price  = $36

Step-by-step explanation:

So

Percent Markup on Cost  (M) = 200% of 12

                                                = 200/100 × 12

                                                = 2 × 12

                                                = $24

Thus the selling price  =  Cost (C) + Markup (M)

                                      = $12 + $24

                                      = $36

Therefore, we conclude that:

The selling price  = $36

Isolate the variable by dividing each side by factors that don't contain the variable.

b = −4

Answer:

B= -4

Step-by-step explanation:

Answer:

(12, 487)

Step-by-step explanation:

y = 3.7x + 442 ----› Eqn. 1

y = 14.4x + 312 ----› Eqn. 2

Substitute y = (3.7x + 442) into eqn. 2.

y = 14.4x + 312 ----› Eqn. 2

3.7x + 442 = 14.4x + 312

Collect like terms

3.7x - 14.4x = -442 + 312

-10.7x = -130

Divide both sides by -10.7

x = 12.1495327

Substitute x = 12.1495327 into eqn. 1.

y = 3.7x + 442 ----› Eqn. 1

y = 3.7(12.1495327) + 442

y = 486.953271

The solution to the system is rounded to the nearest integer:

(12, 487)

Answer:

[(7+3).5-4]/2+2

[46]/2+2

23+2

25

Answer: 25

Step-by-step explanation:

Follow the order of operations: PEMDAS

[(7+3) * 5-4] / 2+ 2

[10*5-4]/2+2

[50-4]/2+2

46/2+2

23+2

= 25

Answer:

1/20

Step-by-step explanation:

3 states start with the letter c. This means that there is a 3/50 probability of getting a state starting with c.

There are 5/6 sides of a die that is at most 5. That is a 5/6 probability.

Multiplying this together, we get:

3/50 x 5/6 =

15/300=

1/20

Answer:

We conclude that:

Step-by-step explanation:

Descartes Rule states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is:

Given the function

[tex]f\left(x\right)=x^4-2x^3-4x^2+2x+3[/tex]

So, the coefficients are 1, −2, −4, 2, 3

As can be seen, there are 2 changes.

This means that there are 2 or 0 positive real roots.

To find the number of negative real roots, substitute x with -x in the given polynomial:

[tex]x^4-2x^3-4x^2+2x+3[/tex]  becomes [tex]x^4+2x^3-4x^2-2x+3[/tex]

The coefficients are 1, 2, −4, −2, 3

As can be seen, there are 2 changes.

This means that there are 2 or 0 negative real roots.

Therefore, we conclude that:

First, [tex]f(x)[/tex] is continuous on its domain, so

[tex]\displaystyle \lim_{x\to\alpha^+} f(g(x)) = f\left(\lim_{x\to\alpha^+} g(x)\right) \\\\ ~~~~~~~~~~~~~~~~~~ = \sin\left(\frac\pi6 \lim_{x\to\alpha^+} \frac{\ln\left(\sqrt x - \sqrt\alpha\right)}{\ln\left(e^{\sqrt x} - e^{\sqrt\alpha}\right)}\right)[/tex]

As [tex]x\to\alpha^+[/tex], [tex]\sqrt x-\sqrt\alpha\to0[/tex] and [tex]e^{\sqrt x}-e^{\sqrt\alpha}\to0[/tex], so overall we have an indeterminate form ∞/∞. Apply l'Hôpital's rule and simplify.

[tex]\displaystyle \lim_{x\to\alpha^+} f(g(x)) = \sin\left(\frac\pi6 \lim_{x\to\alpha^+} \frac{\frac1{2\sqrt x\left(\sqrt x - \sqrt\alpha\right)}}{\frac{e^{\sqrt x}}{2\sqrt x\left(e^{\sqrt x} - e^{\sqrt\alpha}\right)}}\right) \\\\ ~~~~~~~~~~~~~~~~~~ = \sin\left(-\frac\pi6 \lim_{x\to\alpha^+} \frac{e^{-(\sqrt x-\sqrt\alpha)} - 1}{\sqrt x - \sqrt\alpha}\right)[/tex]

Substitute [tex]y=\sqrt x-\sqrt\alpha[/tex], so that [tex]x\to\alpha^+\implies y\to0^+[/tex].

[tex]\displaystyle \lim_{x\to\alpha^+} f(g(x)) = \sin\left(-\frac\pi6 \lim_{y\to0^+} \frac{e^{-y} - 1}y\right)[/tex]

The remaining limit is the right-derivative of [tex]e^{-y}[/tex] at [tex]y=0[/tex], so

[tex]\displaystyle \lim_{x\to\alpha^+} f(g(x)) = \sin\left(-\frac\pi6\frac{de^{-y}}{dy}\bigg|_{y\to0^+}\right) \\\\ ~~~~~~~~~~~~~~~~~~ = \sin\left(\frac\pi6\right) = \boxed{\frac12}[/tex]

It is cheaper for a customer to purchase the first plan if they make more than 300 minutes of long-distance calls. The answer is (C) 300.

Let's denote the number of minutes of long-distance calls as x. Then, the total cost of the second plan would be:

Cost of Plan 2 = $10 + $0.05x

The total cost of the first plan is always $25, regardless of the number of minutes of long-distance calls.

So we need to find the value of x at which the cost of Plan 2 exceeds the cost of Plan 1, i.e. when:

$10 + $0.05x = $25

Subtracting $10 from both sides, we get:

$0.05x = $15

Dividing both sides by $0.05, we get:

x = 300

So for values of x greater than 300, the cost of Plan 2 will exceed the cost of Plan 1.

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The expression which could not be used to calculate the total cost of book purchased by 27 students will be 7(20)+7(7) and 7(30)-7(7)  which is option (a) and (b) .

We have given the cost of the book $7 .

Total cost = Cost per book × Total number of students

                 = 7 × 27

                 =  189

(a) 7(20)+7(7) = 140 - 49

                     = 91

On simplifying the expression , we get 91 which is not equal to the total cost 189 . Hence , this expression does not represent the total cost.

(b) 7(30)-7(7) = 210 - 29

                     = 181

On simplifying the expression , we get 181 which is not equal to the total cost 189 . Hence , this expression does not represent the total cost.

(c) 7(30)-7(3) = 210 -21

                     = 189

On simplifying the expression , we get 189 which is equal to the total cost 189 . Hence , this expression represent the total cost.

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Jim is correct. Jim new mean wage of these workers will be more than £415

The average pay received by workers for doing the same job over a specific time period is known as the mean wage. We can calculate the mean salary by adding up all the salaries paid to workers in a particular industry or occupation, then dividing the result by the total number of workers. The average or mean is equal to (a+b+c)/3.

According to the given value;

Mean wage

= [(320 X10 ) + (370 x 13 ) + ( 420x8 ) + (4 70 *7 )+ ( 520 x 2 )]/40

= (3200+ 4810 + 3360 + 3290+ 1040)/40

=£392.5

. : New mean wage

= £ 392.5 x 104/100+10

= £418.2 > £415

Hence, Jim is correct .

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Answer:

A. Z = 2 + N13

Step-by-step explanation:

Let's solve your equation step-by-step.

0=z2+4z−9

Step 1: Subtract z^2+4z-9 from both sides.

0−(z2+4z−9)=z2+4z−9−(z2+4z−9)

−z2−4z+9=0

For this equation: a=-1, b=-4, c=9

−1z2+−4z+9=0

Step 2: Use quadratic formula with a=-1, b=-4, c=9.

z=

−b±√b2−4ac

2a

z=

−(−4)±√(−4)2−4(−1)(9)

2(−1)

z=

4±√52

−2

z=−2−√13 or z=−2+√13