Answer:
The quotient of these numbers is 1.7 × 10⁴
Scientifically in the notion, these would be the correct numbers.
The quotient of the given numbers is 1.7×10⁴.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.
The given numbers are 7.14×10⁷ and 4.2×10³.
Here, quotient = 7.14×10⁷ ÷ 4.2×10³
= 1.7×10⁴
Therefore, the quotient of the given numbers is 1.7×10⁴.
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based on the experimental probability about how many times will yosef draw a green marble if he draws a total of 75 marbles
Evaluate the function graphically.
Find f(3)
x = y - 4
-2x + 3y= 6
Solve each system by equation
Answer:
Point form=(-6,-2)
Equation Form= x=-6, y=-2
Step-by-step explanation:
An isosceles trapezoid has vertices at (-2, 1), (2, 1), (5, -1) and (-5, -1). find the measure of each diagonal
Check the picture below.
well, is an isosceles trapezoid, namely the slanted sides are equal, so the diagonals, in red, are also equal, so let's just find the length of the solid line diagona, since the dashed one will be the same length anyway.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[2 - (-5)]^2 + [1 - (-1)]^2}\implies d=\sqrt{(2+5)^2+(1+1)^2} \\\\\\ d=\sqrt{7^2+2^2}\implies d=\sqrt{53}\implies d\approx 7.28[/tex]
Please help me ! Reduced to lowest terms
Answer:
Step-by-step explanation:
7) 2ab + 4ac = 2*a*b + 2 *2 *a*c
= 2a(b + 2c)
[tex]\dfrac{2ab^{2}c}{2ab+4ac}=\dfrac{2*a* b^{2}*c}{2a(b+2c)}\\\\\\\text{2a in the denominator and numerator get cancelled}\\\\ = \dfrac{b^{2}c}{b+2c}[/tex]
8) ac - a²c² = c( a - a²c)
bc - abc = c(b - ab)
[tex]\dfrac{ac - a^{2}c^{2}}{bc-abc^{2}}=\dfrac{c(a-a^{2}c)}{c(b-ab)}\\\\[/tex]
[tex]=\dfrac{a-a^{2}c}{b-abc}[/tex]
9) b²+ 4b - 5 = b² + 5b - 1b - 5
= b(b + 5) - 1(b + 5)
= (b +5)(b - 1)
b² + 8b + 15 = b² + 5b + 3b + 15
= b(b + 5) + 3(b + 5)
= (b + 5 )(b + 3)
[tex]\dfrac{b^{2}+4b-5}{b^{2}+8b+15}=\dfrac{(b+5)(b-1)}{(b+5)(b+3)}\\\\\\[/tex]
[tex]=\dfrac{b-1}{b+3}[/tex]
Help me plss
4b(9b^5+7b^4)
Step-by-step explanation:
Step by Step Solution

STEP1:Equation at the end of step 1
STEP2:
22b5 Simplify ———— 9b
Dividing exponential expressions :
2.1 b5 divided by b1 = b(5 - 1) = b4
Final result :
4b4 ——— 9
Ivanna needs to buy some pencils. Brand A has a pack of 36 pencils for 8.52 . Brand B has a pack of 48 pencils for 9.98 . Find the unit price for each brand. Then state which brand is the better buy based on the unit price. Round your answers to the nearest cent.
Answer:
Brand B is better
Step-by-step explanation:
Brand A's unit price is $0.24
Brand B's unit price is $0.21
A mother shared $400 amongst her three daughters Amy, Beatrice and Claire in the ratio of 3:2:5 respectively. How much money did Amy receive?
Answer:
$120
Step-by-step explanation:
Total Parts = 3+2+5 = 10
400 / 10 = $40 per part
Amy = 40 x 3 = 120
A politician estimates that 61% of his constituents will vote for him in the coming election. How many constituents are required for a random sample to obtain a margin of error of at most 0. 03 with 95% confidence
Using the z-distribution, as we are working with a proportion, it is found that 1016 constituents are required.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The estimate is of [tex]\pi = 0.61[/tex], while the margin of error is of M = 0.03, hence solving for n we find the minimum sample size.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.61(0.39)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.61(0.39)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.61(0.39)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.61(0.39)}}{0.03}\right)^2[/tex]
[tex]n = 1015.5[/tex]
Rounding up, 1016 constituents are required.
More can be learned about the z-distribution at https://brainly.com/question/25890103
someone help me please
Answer:
x ≈ 5.8 degrees
Step-by-step explanation:
the sum of all exterior of any polygon is 180 degrees
so: 7x+4 + 5x+4 + 4x+9 + 9x-6 + 4x+1 = 180
combine 'like terms':
29x + 12 = 180
29x = 168
x ≈ 5.8
a
April has a sheet of paper that is 3 feet long. She cuts the length of paper into halves and then cuts the
1
length of each of these pieces into sixths.
2
How many pieces does she have?
How many inches long is each piece?
April has
pieces.
Each piece is
inches long.
Answer:
6x3=18 pieces
6/18 = 1/3
=
18 pieces
72 inches
What is an estimate of 37.9% of 192.3?
A 57
B 02
C 80
D 100
Answer:
C.80
Step-by-step explanation:
37.9% of 192.3
=37.9/100 × 192.3
=0.379×192.3
=72.8817
≈80 (possible answer)
factorise: x^4– 5x^2 + 4
Answer:
(x - 2)(x - 1)(x + 1)(x + 2)
Step-by-step explanation:
[tex] {x}^{4} - 5 {x}^{2} + 4 \\ \\ = {x}^{4} - 4 {x}^{2} - {x}^{2} + 4 \\ \\ = {x}^{2} ( {x}^{2} - 4) - 1( {x}^{2} - 4) \\ \\ = ( {x}^{2} - 4)( {x}^{2} - 1) \\ \\ = (x + 2)(x - 2)(x + 1)(x - 1) \\ \\ = (x - 2)(x - 1)(x + 1)(x + 2)[/tex]
Answer:
[tex](x+1)(x-1)(x+2)(x-2)[/tex]
Step-by-step explanation:
To factorise [tex]x^4-5x^2+4[/tex] :
Let [tex]x^2=u[/tex]
[tex]\implies x^4-5x^2+4=u^2-5u+4[/tex]
Now factorise [tex]u^2-5u+4[/tex]
[tex]\textsf{for} \ ax^2+bx+c \ \textsf{find} \ v, w \ \textsf{such that} \ v \cdot w=a \cdot c \ \textsf{and} \ v+w=b[/tex]
[tex]\textsf{and group into} \ (ax^2+vx)+(wx+c)[/tex]
[tex]\implies v=-1, w=-4[/tex]
[tex]\implies u^2-u-4u+4[/tex]
Break into groups
[tex]\implies (u^2-u)+(-4u+4)[/tex]
Factor each parentheses:
[tex]\implies u(u-1)-4(u-1)[/tex]
Factor out common term [tex](u-1)[/tex]:
[tex]\implies (u-1)(u-4)[/tex]
Substitute back [tex]u=x^2[/tex] :
[tex]\implies (x^2-1)(x^2-4)[/tex]
Factor both parentheses using the Difference of Two Squares: [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]\implies (x+1)(x-1)(x+2)(x-2)[/tex]
Therefore, the factorisation of [tex]x^4-5x^2+4[/tex] is
[tex](x+1)(x-1)(x+2)(x-2)[/tex]
their sum is -11 and difference is 41
Answer:
15 and -26.
Step-by-step explanation:
Answer:
15 and -26
Step-by-step explanation:
just bc
Need help with this, I’ll give brainliest for an explaining response :)
Answer:
d
Step-by-step explanation:
The answer must be a multiple of 4, because 4q⁵rs⁴ is divisible by 4. Only option d has this condition.
Please help me graph the points with this please and thank you
Answer:
Hope this helps <3
Step-by-step explanation:
(I color coded them and named them for you so that you wouldn’t have trouble with finding the points <3)
A construction company transported 8 stones that weighed a total of 70.22 kilograms. How much did each stone weigh?
Answer:
8.7kilos
Step-by-step explanation:
70.22 divided by 8
hope this helps!
Please answer I am stuck on this problem
Answer:
20+2C
Step-by-step explanation:
sum means addition
if Craig's age is c than twice his age is 2xC, also expressed as 2C
20+2C
A circular swimming pool has a radius of 20 feet. The family that owns the pool wants to put up a circular fence that is 5 feet away from the pool at all points. Which is closest to the circumference of the fence they will need?
Answer:
157.08 ft
Step-by-step explanation:
R = 20+5 = 25
Circumfrence = 2*pi*r = 2*pi*25 = 157.079 ft
32+4 X (16 X ) -2 show your work
Answer:
32+4x(16x)-12=
32+64x-12=
64x-12+32=64x+20
64×÷64÷=20÷64=
x=0.3125
1. Find the Area of the Sector:
2. Find the length of the missing side:
1. Area of sector is 14.14 sq.m
2. Length of the missing side is 10 cm
Step-by-step explanation:1.)Using formula:
Area of sector = θ/360° × π r²Where,
θ = 45° Radius (r) = 6mSubstituting the required values:
→ Area = 45°/360° × 22/7 × (6)²
→ Area = 0.125 × 22 × 36/7
→ Area = 2.75 × 36/7
→ Area = 99/7
→ Area = 14.14 sq.m
2.)In given right angled traingle:
Perpendicular = 6 cmBase = 8 cmHypotenuse = ?Using Pythagoras theorem,
(H)² = (B)² + (P)²where,
H is hypotenuseB is Base P is perpendicularSubstituting the required values:
→ (Hypotenuse)² = (8)² + (6)²
→ (Hypotenuse)² = 64 + 36
→ (Hypotenuse)² = 100
→ Hypotenuse = √100
→ Hypotenuse = 10 cm
Hence,
Hypotenuse of Traingle is 10 cmfind the volume of a right circular cone that has a height of 3.2 m and a base with a radius of 14.1 m
Answer: 666.22 m^3
Step-by-step explanation:
The formula for the volume of a right circular cone is: V = π*r^2*(h/
3)
Therefore, plugging in 14.1 for "r" and 3.2 for "h" yields 666.22
what numbers can you make ?
Answer:
196
Step-by-step explanation:
solve for x:
-3(x-2)^2+17=0
round your answer to the nearest hundredth
Answer:
-3(x-2)×2+17=0
-3x+6×2+17=0-3x+12+17=0-3x+29=0-3x=0-29=-29-3x=-2929÷3=9.700 to the nearest hundredthStella's monthly bank statement showed the following deposits and withdrawals: − −$34.71, − −$100.08, $111.62, $92.93, − −$27.27 If Stella's balance in the account was $20.1 at the beginning of the month, what was the account balance at the end of the month?
Answer: $ 27.27
Step-by-step explanation:
Answer:
62.59
Step-by-step explanation:
Manny has car insurance and was in an accident with a bill totaling $11,500. The insurance company says he needs to pay the first $1000. What does the $1000 represent?.
Answer:
Deductible
Step-by-step explanation:
you pay the first $1,000 of covered services yourself
$1000 represents the deductible amount.
In the case of an accident, the policyholder must pay a deductible as the first amount; the insurance company will only cover any expenses (losses) incurred after the deductible has been paid by the policyholder.
The consumer can first set his deductible while purchasing insurance.
Smaller deductibles often result in higher rates, and larger deductibles frequently result in lower premium payments.
The insurance company has asked Manny to pay the first $1000 in an instance when he was involved in an accident and incurred charges totaling $11,500. The $1,000 deductible amount.
Hence, the answer is deductible amount.
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ixl math question im very lazy and i dont understand
Answer:
1/21
Step-by-step explanation:
We start with 7 cards. The probability of picking a 4 is 1/7. Since the first card is not put back, there are 6 cards left. Of these 6 cards, there are two which have divisors of 63: 3 and 7. So the probability of picking a divisor of 63 is 2/6, which reduces to 1/3. Multiplying these probabilities gives 1/21.
Which statements are true for the following expression?
(9 + 1) · 5
Answer:
50
Step-by-step explanation:
add
9 + 1 = 10
multiply
10 * 5 = 50
Answer: 50
Katie practiced her flute for 45 mins Then she ate a snack for 15 mins Next She watched televosion for 30 mins until 6:00 p.m at what time did Katie start practicing the flute
find the value of x
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{11 + x}\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{17}\\ \end{cases}\implies (11+x)^2=x^2+17^2 \\\\\\ (11+x)(11+x)=x^2+17^2\implies \stackrel{F~O~I~L}{121+22x+x^2}~~ = ~~x^2+289 \\\\\\ 121+22x=289\implies 22x=168\implies x=\cfrac{168}{22}\implies x=\cfrac{84}{11}\implies x=7\frac{7}{11}[/tex]