The rounding of the numbers to 1 significant figure are-
a) 687 × 164 = 140000
b) 476 × 2354 = 1000000
c) 8612 × 1497 = 9000000.
What is defined as the significant figure?The term significant figures describes the number of significant single digits (0 to several 9 inclusive) in a scientific notation coefficient. The number of significant figures inside an expression indicates the degree of certainty or precision with where an engineer or scientist states a number.All zeros to the right of the decimals but to the left of a non-zero number in a decimal number between 0 and 1 are not significant. 0.00247, for example, only has three significant figures.a) 687×164
This number can be written in form of rounding to 1 significant figure as;
700 × 200 = 140000
b) 476×2354
As, the number can be written in form of rounding to 1 significant figure as;
500 × 2000=1000000
c) 8612×1497
These number can be written in form of rounding to 1 significant figure as;
9000×1000=9000000
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Please please help me!!!!!
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)
HELP the bag of letter tiles include 15 vowels and 25 consonants. What is the probability of selecting two vowels one after another? NEED HELP ASAP
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.
Bank D pays 7.289% effective annual yield, on an investment account in which interest is compounded weekly. What is the annual interest rate before compounding?
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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plz help what is the square root of pi
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 ....
Let [tex]R[/tex] be the region bounded between the parabola [tex]y=4x-x^2[/tex] and the x-axis. Find [tex]m[/tex] so that the line [tex]y=mx[/tex] divides [tex]R[/tex] into two pieces of equal area.
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]
Simplify 8 over negative 4 ÷ negative 3 over 9 . (5 points)
Answer:
6
Step-by-step explanation:
[tex]-\frac84 divided-\frac39\\-2 divided- \frac13\\-2 \cdot -3\\6[/tex]
Geometry. PLS help asap 20 points
Answer:
you need to prove AB=AD
Step-by-step explanation:
help me please with this math problem [(7 + 3) • 5 – 4] ÷ 2 + 2
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
How do I use the Descartes Rule of Signs to determine all possible number of positive and negative zeros?
f(x)= x^4-2x^3-4x^2+2x+3
Answer:
We conclude that:
2 or 0 positive real roots2 or 0 negative real rootsStep-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:
Either equal to the number of sign differences between consecutive nonzero coefficients, Or is less than it by an even number.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:
2 or 0 positive real roots2 or 0 negative real rootsJenna❤️Jenna❤️❤️L’s recipe calls for 1/2 cup of flour she only has 1/4 cup measure which equivalent fraction shows the amount of flowers she could use for the recipe
Answer:
1/2 divided by 1/4
Step-by-step explanation:
so 2
hope this helps :)
A phone company has two long distance
calling plans. The first plan is $25 per month
for unlimited long distance calling. The second
plan is $10 per month plus $0.05 per minute
of long distance calling. After how many
minutes oflong distance calls will it be cheaper
for a customer to purchase the first plan?
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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2x^2 - 3x - 2 = X + 4
The equation is represented by the system shown
here.
Check all of the solutions to this equation
-1, 3, 7, (-1, 3), (3, 7)
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).
What is a quadratic function?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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Let X denote the number of cousins of a randomly selected student. Explain the difference between StartSet Upper X equals 2 EndSet and Upper P (Upper X equals 2 ).
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.
B. (X =4) is the frequency that a student has four cousins, P(X-4) is the relative frequency that a student has for cousins.
C. (X =4) is the probability of the event that the student has four cousins, P-4) is the event that the student has four cousins.
D. (X =4) is the relative frequency that a student has four cousins; P(X 4) is the frequency that a student has four cousins.
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.
$2,000 lounge suite was sold under a hire purchase agreement. A deposit of $200 was made. The balance and interest were then paid off in equal monthly instalment of $68 over 3 years.
How much did the lounge suite cost in total?
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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A farm has 216 apple trees. The trees were evenly across 8 rows. How many apple trees are there in each row
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
A clothing store buys jeans for $12 and marks them up 200% before selling them to customers. What is the selling price of the jeans? Group of answer choices
Answer:
The selling price = $36
Step-by-step explanation:
The Buying price or Cost (C) = $12Markup = 200%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
Write the equation of each graph. Will give Brainliest to correct answer!
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]
5. Jade has $59.87 in her checking account.
She buys his mom a birthday present for $25.98.
How much money is left in her account?
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
12) Jim owns a small business.
The table shows information about the weekly wage of the 40 workers
Weekly wage (£)
320
370
420
470
520
Number of workers
10
13
8
7
2
Jim wants to increase the mean wage by 4%, plus £10
Jim thinks the new mean weekly wage of these workers will be more than £415
Is Jim correct?
(6)
Jim is correct. Jim new mean wage of these workers will be more than £415
What is MEAN WAGE?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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A recipe for punch uses 2 cups of grape
juice and 3 cups of orange juice. How many
cups of orange juice are needed if 6 cups of
grape juice are used?
A 7 cups
B 9 cups
C 15 cups
D 30 cups
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.
5. Solve the equation z^2 + 4z - 9 = 0 by completing the square.
A. Z = 2 + N13
B. Z= 4 + 113
C. Z=-2 + V13
D. z = -4 + 13
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
What is the point of factoring
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.
in Chad‘s reading class all the students are reading the same book the school body student the book at seven dollars per book if there are 27 students in Chad‘s class which of the following expressions could not be used to calculate the total cost 7(20)+7(7) 7(30)-7(7) 7(30)-7(3)
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) .
An expression or algebraic expression is a mathematical statement consisting of numbers, variables and arithmetic operations between them.In order to find the cost of many items from the cost of 1 item, we apply multiplication operation.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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A builder can buy 6 sheets of plywood for $33. At that rate, how much would 14 sheets of plywood cost?
Answer: 77 dollars
Step-by-step explanation:
6 sheets = 33 dollars
14 sheets = {(33/6)*14} = 77 dollars
Petro was given this system of equations. Negative 14 x minus 2 y = 24. 14 x + 8 y = negative 12. Petro’s work is shown in the table. Where, if anywhere, did Petro first make a mistake? Steps Petro’s Work Step 1 Negative 14 x minus 2 y = 24. 14 x + 8 y = negative 12. 6 y = 12. Step 2 6 y = 12. y = 2. Step 3 Negative 14 (2) minus 2 y = 24. Negative 28 minus 2 y = 24. Negative 2 y = 52. y = negative 26.
step 1
step 2
step 3
no mistake
Answer:
C Step 3
Step-by-step explanation:
Answer:
C: Step 3 is where the mistake was made
Step-by-step explanation:
if a substance has a half life of one day and an initial amount of 100 grams, how many grams will be left after 2 days
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
b - 7(b + 2) = 10
can someone solve this?
Isolate the variable by dividing each side by factors that don't contain the variable.
b = −4
Answer:
B= -4
Step-by-step explanation:
Let [tex]\alpha[/tex] be positive real number.
Let f:[tex]\mathbb{R}\to\mathbb{R}[/tex] and g:[tex](\alpha,\infty)\to\mathbb {R}[/tex] be the function defined by
[tex] \rm f(x) = \sin \bigg( \dfrac{\pi x}{12} \bigg ) \: and \: g(x) = \dfrac{2 log_{e}( \sqrt{x} - \sqrt{ \alpha } ) }{ log_{e}( {e}^{ \sqrt{x} } - {e}^{ \sqrt{ \alpha } } ) } [/tex]
Then the value of [tex] \rm \lim_{x \to { \alpha }^ + } f(g(x)) \\ [/tex] is
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]
HELPP PLEASE WILL GIVE BRAINLIEST
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
Explain two attributes that a rectangle and a square have in common.
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: