Answer:
x = 1.5 +/-√3.25.
Step-by-step explanation:
x^2 - 3x - 1 = 0
x^2 - 3x = 1
Completing the square:
(x - 1.5)^2 - 1.5^2 = 1
(x - 1.5)^2 = 1 + 2.25 = 3.25
x - 1.5 = +/-√3.25
x = 1.5 +/-√3.25
Suppose you invest $9270 at an annual interest rate of 5.3% compounded continuously.
How much will you have in the account after 34 years?
Answer:
$54659.21
Step-by-step explanation:
By using the formula of 9270 * (1.053)^34 I can find the annual compound interest.. I reccomend using a calculator.
if 2 X + 1 ,2 x-1 and 3 X + 4 are in AP find the value of x
Answer:
x = - 7
Step-by-step explanation:
Given that the terms are in AP , then
a₃ - a₂ = a₂ - a₁ , substitute values
3x + 4 - (2x - 1) = 2x - 1 - (2x + 1) ← distribute and simplify both sides
3x + 4 - 2x + 1 = 2x - 1 - 2x - 1
x + 5 = - 2 ( subtract 5 from both sides )
x = - 7
Find the circumference of the pizza 18in to the nearest hundredth. circumference: about in.
Answer:56.55
Step-by-step explanation:
2 x pi x radius which is half of 18 so 9 is about 5.487 and rounded to the nearest hundredth is 56.55.
PLSSSS HELLPPPPP!!!
Answer: B, D, and F
Step-by-step explanation:
Hi, so for this question, the phone bill is in an equation. Before doing this problem, make sure to understand what the 2 and 56 mean. The problem says that c is the monthly charge, and m is the number of minutes. This means that 2 is the number of dollars required to pay when you use the phone for one minute. So 2 dollars per minute. The 56 is basically the fee that is just charged for using the phone bill. Meaning that even if you don't use the phone at all, you will still need to pay 56 dollars.
By understanding those info, it should be easier to answer.
For A, it is not correct. if you look, although 2*4 is 8 dollars, but you need to add 56 for the monthly bill. (I think when they say 'your bill' they mean the monthly bill).
For B, it is correct. Like I said before, the 56 dollars is there no matter how long you use the phone.
For C, it is not correct. This isn't hard to understand since if B is correct, C is probably not, and vise versa. And the 56 dollars is missing.
For D, it is correct. As I said before, the 2 represents the amount of dollars for one minute.
For E, it is not correct. (Contradicts the previous answer and each minute costs 2 dollars).
For F, it is correct. When you use 2 minutes, the equation is 2*2+56 which is 60 dollars.
Hopefully this helps!
In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,911 of them had no strategic business plan. a) Use a 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans. Give an interpretation of this interval. (5 Points) b) Would a 99% confidence interval be wider or narrower than the one you calculated in part (a)
Answer:
a) The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.
b) Wider
Step-by-step explanation:
Question a:
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].
In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,911 of them had no strategic business plan.
This means that [tex]n = 3900, \pi = \frac{1911}{3900} = 0.49[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 - 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.4768[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 + 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.5032[/tex]
The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.
Question b:
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The higher the confidence level, the higher the value of z, thus the higher the margin of error and the interval is wider. Thus, a 99% confidence interval is wider than a 90% confidence interval.
Which set of values could be the side lengths of a 30-60-90 triangle?
O A. {6, 12, 12 3 }
O B. {6,62,12}
O C. {6, 12, 12.12}
O D. {6,6,13,12}
Answer:
my only question is A
Step-by-step explanation:
when you have a 30-60-90 triangle, you sides will always have a set pattern
Answer: A) {6, 12, 12 3 }
explanation: The sides of a 30-60-90 triangle will always have a consistent design. Thus, the answer is A.
Based on the density graph below, what is the probability of a value in the sample space being anywhere from 10 to 25?
A. 80% B. 60% C. 40% D. 20%
The probability of the sample from 10 to 25 will be 60%. Then the correct option is B.
What is probability?Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.
Based on the density graph below.
Then the probability of a value in the sample space being anywhere from 10 to 25 will be
P = (25 - 10)/(25 - 0)
P = 15/25
P = 0.6
P = 60%
Thus, the probability of a value in the sample space being anywhere from 10 to 25 will be 60.
Hence the correct option is B.
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Please help on this...
Fine the perimeter and the area of this.
Answer:
p = 18 in
a = 25 in²
Step-by-step explanation:
perimeter = sum of the sides
p = 4 1/3 + 5 1/3 + 8 1/3
p = 18 in
Area = 1/2 * base * height
a = 1/2 * 8 1/3 * 6
a = 1/2 * 50
a = 25 in²
Answer:
[tex]p=18\:\mathrm{in},\\A=25\:\mathrm{in^2}[/tex]
Step-by-step explanation:
The area of a triangle is given by [tex]A=\frac{1}{2}\cdot b\cdot h[/tex]. By definition, the base and height must intersect at a [tex]90^{\circ}[/tex] angle.
In this diagram, we notice that the lengths [tex]8\frac{1}{3}[/tex] and [tex]6[/tex] intersect at a [tex]90^{\circ}[/tex], so we can use them as the base and height of the triangle, respectively.
Therefore, the area of the triangle is equal to:
[tex]A=\frac{1}{2}\cdot 6\cdot 8\frac{1}{3}=3\cdot \frac{25}{3}=\boxed{25\:\mathrm{in^2}}[/tex].
The perimeter is simply the sum of all sides of the triangle. Thus, we have:
[tex]p=4\frac{1}{3}+8\frac{1}{3}+5\frac{1}{3}=4+8+5+1=\boxed{18\:\mathrm{in}}[/tex]
A coin is tossed twice. Let Z denote the number of heads on the first toss and W the number of heads on the second toss. If the coin is unbalanced and a head has a 40% chance of occurring, find
Answer:
0.64
Step-by-step explanation:
Prob ( Head ) = 40% = 0.4 , Prob ( Tail ) = 1 - 40% = 60% = 0.6
4 outcomes = (Head Tail) , (Tail Head) , (Head Head) , (Tail , Tail)
Prob (Atleast one head) = Pr (Head Tail) + Pr (Tail Head) + Pr (Head Head)
(0.4) (0.6) + (0.6) (0.4) = 0.24 + 0.24 + 0.16 = 0.64
A chemist mixes 25 milliliters of a solution that is 44% acid with 225 milliliters of pure acid.
(a) How many milliliters of acid are in the resulting
mixture?
milliliters
(b) What percentage of the resulting mixture is acid?
Answer: a) 236 ml b) 94.4 %
Step-by-step explanation: a) in 44 % solution there is 0.44 · 25 ml = 11 ml.
Total volume of acid is 225 ml + 11 ml = 236 ml
b) vol-% of acid is 236 ml /(225 ml + 25 ml) · 100 % = 94.4 %
The milliliters of acid that are in the resulting mixture is 236 millimeters and the percentage of the resulting mixture is acid is 94.4%.
a. The milliliters of acid are in the resulting mixture will be:
= 225 ml + (44% × 25ml)
= 225ml + (0.44 × 25ml)
= 225ml + 11ml
= 236ml
b. The percentage of the resulting mixture that is acid will be:
= [(236ml / (25ml + 225ml)] × 100
= (236ml/250ml) × 100
= 94.4%
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PLEASE ANSWER 10 POINTS
what is the probability of rolling either a two or a three on a six sided number cube
A theater has 35 seats in the first row. Each row has four more seats than the row before it. Which expression represents the number of seats in the nth row?
Answer:
35x4
Step-by-step explanation:
PLZ Help ASAP I Dont understand
2 y determinant is the answer
Lawns by Brawns uses 13 ounces of fertilizer for 6.5 acres. Assume the company is fertilizing 0.5 of an acre. How much fertilizer does it need
Amount of fertilizers required for 0.5 acres = 1 onces.
What is unitary method?Unitary method is a process with the aid of which we discover the fee of a unmarried unit from the cost of multiple units and the cost of a couple of gadgets from the fee of a unmarried unit. it's far a method that we use for most of the calculations in math.
The technique wherein first we discover the fee of one unit after which the price of the desired wide variety of devices is known as the Unitary method.The formula for unitary approach is to find the price of a unmarried unit after which locate the value of extra or fewer devices by way of multiplying their quantity with the value of a unmarried unit.
In case we are having the cost of multiple items with us, then we are able to genuinely divide the entire cost with the quantity of units to get the price of 1 unit and this technique is known as the unitary method. In easy terms, the unitary method is used to locate the cost of a unmarried unit from a given multiple.
Unitary approach is the technique via which we discover the value of a unmarried unit from the value of multiple units and then use this price to locate the cost of the specified wide variety of devices. cost of many devices.
explanation;
13 0nces of fertilizers required for 6.5 acres
for 1 acres land = 13 / 6.5
onces of fertilizers required = 2 onces
for 0.5 acres = 2 *0.5 = 1 onces of fertilizers required.
Hence required fertilizers = 1 onces.
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Here is a list of numbers:
3,16, 7, 19, 1, 12, 3,9,16,12
State the median.
Answer:
10.5
Step-by-step explanation:
Answer:
Step-by-step explanation:
3,16, 7, 19, 1, 12, 3,9,16,12
First list in ascending order:
= 1 3 3 7 9 12 12 16 16 19
The median is the mean of the middle 2 numbers:
Median = (9 + 12) / 2 = 10.5.
what is the volume measured in cubic centimeters, of the box below? do not include units in your answer
Answer:
60
Step-by-step explanation:
V = lwh
V= 4x3x5
V=60
Answer:
Solution given:
l=4cm
b=3cm
h=5cm
volume=l*b*h=4*3*5=60cm³
Find the measure of each angle indicated (quadrilaterals)
I think it’s 100 I just wanna make sure if it is
Find the measure of each angle indicated.
○ 44°
○ 68°
○ 59°
○ 100°
____________________Solution :-Given Information :-∠S = 95° ∠T = 85° ∠Q = 80° To Find :-The measure of ∠R Formula Used :-Sum of all angles of a Quadrilateral = 360° Calculation :-We will simply substitute the given values in the formula,
⇒ Sum of all angles of a Quadrilateral = 360°
⇒ ∠S + ∠T + ∠Q + ∠R = 360°
Substituting the values given, We get,
⇒ 95° + 85° + 80° + ∠R = 360°
Calculating further, We get,
⇒ 260° + ∠R = 360°
Transposing 260° to Right Hand Side, We get,
⇒ ∠R = 360° - 260°
Calculating further, We get,
⇒ ∠R = 100°
∴ ∠R = 100°
____________________Final Answer :-The measure of ∠R is 100°
Hence, Last option i.e., 100° is correct answer.
____________________9. Simplify 1/2 (4a + b) - 1/4 (4a + b)
А. a
B. a + 1/4 b
C. 2a + 1/4 b
D. 2a - b
B: a+ 1/4b Hope this helps!
B. [tex]a + \frac{1}{4} b[/tex] ✅
Step-by-step explanation:
[tex] \frac{1}{2} (4a + b) - \frac{1}{4} (4a + b) \\ = \frac{4a + b}{2} - \frac{4a + b}{4} \\ = \frac{2(4a + b)}{2 \times 2} - \frac{4a + b}{4} \\ = \frac{8a + 2b}{4} - \frac{4a + b}{4} \\ = \frac{8a + 2b - 4a - b}{4} \\ = \frac{4a + b}{4} \\ = \frac{4a}{4} + \frac{b}{4} \\ = a \: + \frac{1}{4} b[/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Find the sum of the first 21 terms of the sequence 5,9, 13, 17, 21, ...
If the graph of a linear equation is translated 4 units down, which statement best describes the change to the equation?
A.The y-intercept of the equation is decreased by 4.
B.The y-intercept of the equation is increased by 4.
C.The slope is changed by a factor of −4
D.The slope is changed by a factor of 4.
The slope is not affected. The y-intercept does not increase. The correct option is A.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
A translation in mathematics moves a shape left, right, up, or down but does not turn it. The translated (or image) shapes appear to be the same size as the original shape, indicating that they are congruent. They've just moved in one or more directions.
Given that if the graph of a linear equation is translated 4 units down. The slope remains unaffected. The y-intercept does not grow.
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write a trigonometric expression for the refracted angle and write the refracted angle in terms of distance d and material width w
Answer: The Diagram of the refracted angle is attached below
answer : ∅ = cos^-1 ( w/d )
Step-by-step explanation:
The trigonometric expression for the refracted angle
with respect to ; Distance ( d ) and width ( w )
Cos ∅ = Adjacent / Hypotenuse ----- ( 1 )
where; adjacent = W . Hypotenuse = d
back to equation 1
Cos ∅ = w / d
∴ ∅ = cos^-1 ( w/d )
Suppose you save $1 the first day of a month, $4 the second day, $16 the third day, and so on. That is, each day you save four times as much as you did the day before. What will you put aside for savings on the seventh day of the month?
Answer:
$ 4096 on the 7th day
Step-by-step explanation:
From the amount earned for the first 3 days it's 1 , 4 , 16 , .... We realize it increases exponentially.
So therefore:
Day 1 =4⁰
Day 2=4¹
Day 3=4²
Day 4=4³
Day 5=4⁴
Day 6=4⁵
Day 7=4⁶
Therefore on day 7 he saves 4⁶ which is $4096
Which of these statements are true?
Select all that apply.
Experimental probability is determined by trials.
Theoretical probability can be any number from 0 to 1.
Experimental probability can be any number from 0 to 1.
Experimental probability is determined by estimating.
Theoretical probability is greater than experimental probability.
Step-by-step explanation:
The theoretical probability is greater than experimental probability
Answer:
Step-by-step explanation:
Experimental probability is determined by trials and Theoretical probability is greater than experimental probability
Sasha is taking cooking class. The total cost in dollars of the classes can be found using the function d = 12.750 + 35, where c is the number of classes attended. Sasha will attend at least one class and no more than eight classes. What is the domain of the situation?
Answer:
[1,8] or 1 [tex]\leq \\[/tex] x [tex]\leq[/tex] 8
Step-by-step explanation:
The domain is number of classes she can/will take, therefore the domain is between 1 and 8.
PLEASE HELPP!!!
Jamie has a $15 iTunes gift card. Songs cost $0.75 and she wants to keep $5 on the
card. How many songs can she download?
a.
Write and solve the inequality that represents Jamie's situation.
b.
Use your inequality to decide how many songs Jamie can download.
Answer:
13
Step-by-step explanation:
starting equation is 15=0.75(x)+5.
You have to have the numbers on one side so...
15-5=10, and 5-5=0.
now, our equation is 10=0.75(x).
we are looking for x, so....
10/.75= 13 and 1/3.
since there is no such thing as a third of a song, 13 would be our number.
Not sure if i already asked this one! Math help please :)
Answer:
Hello again!
Original coordinates: 5, -2
New coordinates: 0, 4
Heres a picture demonstration to find the new coordinates. How I moved 5 left and 6 up
Hope that helps!
Gail works for Ice Cream To-Go. She needs to fill the new chocolate dip cones completely with vanilla ice cream, so that it is level with the top of the cone. Gail knows that the radius of the inside of the cone top is 25 millimeters and the height of the inside of the cone is 129 millimeters.
Using 3.14 for , how much vanilla ice cream will one chocolate dip cone hold when filled to be level with the top of the cone?
Answer:
In other words, they want you to find the volume of the cone.
Volume of a cone=1/3 (pi * radius^2 *h)
Volume=1/3 [3.14* (22)^2 * 120]
Volume=1/3 (3.14*484*120)
Volume=1/3 (182371.2)
Volume= 182371.2/3
Volume=60790.4
The volume of the cone is 60790.4mm^3
But that is not the final answer. Since liquid is measured in litres, You need to convert it to millilitres. So the answer is that one chocolate dip cone can hold a maximum of 60.9704 milliliters
Step-by-step explanation:
Hope this helps
5. Jon Metcalf signed a 253-day simple interest note for $7700 with a bank that uses exact interest. If the rate is 10 3/4% find the maturity value.
Answer:
8281.72
Step-by-step explanation:
Given:
Principal, P = 7700
Rate, r = 10 3/4 % = 43/4 % = 0.1075
Time, t = 253 days = 253/ 360
Using the relation :
A = P(1 + rt)
A = maturity value
A = 7700(1 + 0.1075*253/360)
A = 7700(1 + 0.0755486)
A = 7700(1.0755486)
A = 8281.7243
A = 8281.72
GEOMETRY HELLP :)))))))))))))))))))))))))))))))))))))))))))))))
Answer:
Step-by-step explanation:
angle S+angle T+angle+angle R=180 degree(being sum of interior angle of a triangle)
4x^2-6x+40+18x+3+2x^2-7=180
6x^2+12x+36=180
6(x^2+2x+6)=180
x^2+2x+6=180/6
x^2+2x+6=30
x^2+2x=24
x(x+2)=24
x+2=24/x
x=24/x-2
x=24-2x/x
substitute the value of x^2 in angle R
2x^2-7
2(24-2x/x)^2-7(here x and x gets cancel)
2(24-2)^2-7
2*22^2-7
2*484-7
968-7
961
Answer:
Step-by-step explanation:
angle S+angle T+angle+angle R=180 degree(being sum of interior angle of a triangle)4x^2-6x+40+18x+3+2x^2-7=1806x^2+12x+36=1806(x^2+2x+6)=180x^2+2x+6=180/6x^2+2x+6=30x^2+2x=24x(x+2)=24x+2=24/xx=24/x-2x=24-2x/xsubstitute the value of x^2 in angle R2x^2-72(24-2x/x)^2-7(here x and x gets cancel)2(24-2)^2-72*22^2-72*484-7968-7961
please help me!!! justify your answers.
Answer:
G is true is out divide 1/7 by 2 out get 1/14
H is false the product is always 1
I is false all numbers have a reciprocal besides 0
Answer:
g. True
h. False
i. False
Step-by-step explanation:
g.
[tex]\frac{1}{14}[/tex] is half of [tex]\frac{1}{7}[/tex]
This would be true because half of a number can be found by multiplying by [tex]\frac{1}{2}[/tex]
If you multiplied [tex]\frac{1}{7} * \frac{1}{2}[/tex]
The numerator is 1 * 1 which is 1
And then the denominator is 7 * 2 which is 14
That would give you [tex]\frac{1}{14}[/tex]
h.
The products of two reciprocals is 0
This is not true
Reason being, reciprocals are just the number flipped. If you times the number by itself, you don't get 0, you get 1.
Ex: [tex]\frac{2}{8}[/tex]
Its reciprocal is [tex]\frac{8}{2}[/tex]
So multiply them together
[tex]\frac{2}{8}* \frac{8}{2}[/tex]
2 * 8 = 16
8 * 2 = 16
[tex]\frac{16}{16} = 1[/tex]
i.
A whole number does not have a reciprocal
This is incorrect. If you think about it, a whole number is just the number, over 1
Ex: [tex]\frac{6}{1}[/tex]
This is still a whole number even though its written in fraction form because if you divide 6 by 1, your still going to get 6.
If you an write it as a fraction, it has a reciprocal.
The reciprocal in this case would be [tex]\frac{1}{6}[/tex]
I hope this helps, don't be afraid to reach out with any further questions!