Answer:
t = 6 years
Step-by-step explanation:
Use the simple interest formula: i = prt, where p is the principal, r is the interest rate as a decimal fraction, and is the elapsed time, in years.
Here we want to know how long it will take for the interest alone to reach $449.40. We first solve i = prt for t, obtaining t = i/(pr).
Here, the length of time is t = ($449.40) / (0.06*$1498.00). This works out to
t = 5.9947, or approximately 6 years.
t = 6 years
Researchers claim that 90% of people are left handed. Suppose the researchers' claim is true. Mrs. Reyes has a Statistics class with 30 students. What is the probability that exactly 25 of them are left handed?
Answer:
10.23% to the nearest hundredth.
Step-by-step explanation:
This is a Binomial Probability Distribution.
If exactly 25 are left handed then exactly 5 are right handed.
So (probability that exactly 25 are left handed)
= 30C5*(0.1)^5(0.9)^25
= 0.1023047706
= 10.23%.
The probability that exactly 25 students out of 30 are left-handed, assuming the researchers' claim is true, is approximately 0.2031, or about 20.31%.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
This problem involves the binomial probability distribution, where we have a fixed number of trials (30 students in this case), and each trial has two possible outcomes (left-handed or not left-handed).
The probability of success (a student being left-handed) is 0.9, based on the researchers' claim.
The probability of a failure (a student not being left-handed) is 1 - 0.9 = 0.1.
We want to find the probability that exactly 25 students out of 30 are left-handed.
This can be calculated using the binomial probability formula:
[tex]P(X = k) = ^nC_ kp^k (1 - p)^{n-k}[/tex]
where:
n = 30 (the number of trials)
k = 25 (the number of successes we want)
p = 0.9 (the probability of success in each trial)
Plugging in the values, we get:
[tex]P(X = 25) = ^{30}C_ {25}~ 0.9^{25} ~0.1^5[/tex]
Using a calculator or statistical software, we can find that:
P(X = 25) ≈ 0.2031
Therefore,
The probability that exactly 25 students out of 30 are left-handed, assuming the researchers' claim is true, is approximately 0.2031, or about 20.31%.
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Solve for x. Round your answer to the nearest tenth if necessary.
70°
6
X
Answer:
Tan 70 = opp/adj
Tan 70 = x/6
multiply by 6 on both sides
16.5 = x
An ice cream shop sells ice cream cones, c, and
milkshakes, m. Each ice cream cone costs $1.50
and each milkshake costs $2.00. Donna has $19.00
to spend on ice cream cones and milkshakes. If she
must buy 5 ice cream cones, which inequality could
be used to determine the maximum number of
milkshakes she can buy?
Answer:
$7.50+m > $19
The inequality to be used for determining the maximum number of milkshakes she can buy will be in the form of:
[tex]\$7.50+\$2.00\rm{m}\leq \$19.00[/tex]
The inequality in the position or the relationship between two variables in order to make the total either greater than, less than, or greater than equal to, or less than equal to the total amount.
The inequality can be between numbers or algebraic expressions.
In the given case,
Per unit cost of ice cream cone $1.50 Per unit cost of milkshakes $2.00 The total amount for spending is $19.00 Number of ice cream cones bought 5To determine the inequality for the number of milkshakes the inequality will be formed as follows:
The total cost of ice cream cones will be added with the total cost of milkshakes (where m is the number of milkshakes) and the sign used will be greater than or equal to the given amount to be spent.
Therefore, the inequality will be [tex]\$7.50+\$2.00\rm{m}\leq \$19.00[/tex]
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Hey guys, i need help on this one, thanks in advance.
Find the slope of the equation:
x - 5 = 3 ( y + 4 ) -2y + 1
if you could add step's please do.
Answer:
slope = 1
Step-by-step explanation:
1) expand those brackets on the left side my multiplying
x - 5 = 3y + 12 - 2y + 1
2) simplify by collecting like terms
x - 5 = y + 13
3) bring -5 to the right side by adding 5
x = y + 18
4) let's rearrange this equation in the form y = mx + c where m is the gradient (slope) and c is the y intercept. by subtracting 18 on both sides
y = (1)x - 18 (there is a 1 in front of the x, but we don't write it like that. m is 1)
y = x - 18
the slope is the gradient, which is 1
Find the missing factor
Answer:
[tex](x^4y^5)(x^2y^4)[/tex]
Step-by-step explanation:
Keep these things in mind:
[tex]x^3\times x^3=x^{3+3}=x^6\\\\(x^3)^3=x^{3\times3}=x^9[/tex]
Using those, simplify the left side of this equation:
[tex](x^2y^3)^3\\x^6y^9[/tex]
Now we know what the exponents need to become, so we can find the difference between those and what we have on the right:
[tex]6-4=2\\9-5=4[/tex]
We need to add a 2 to the x, and add a 4 to the y.
[tex](x^4y^5)(x^2y^4)[/tex]
Marks test scores for this semester were 83,80,91,74,66,95,87,72,95,97 what is the mode of his test scores
Answer:
95
Step-by-step explanation:
Mode is what is the most frequent number that occurred; 95 occurred the most from the data.
Sally is paid to walk her neighbor’s dog every day.Every month she is paid she puts away $20 and saves the rest.Write an expression that represents the amount she will save in 6 months if she earns m dollars each month.If she’s paid $65 each month how much will she save in 6 months?
Answer: she would have saved 120$$
Step-by-step explanation:
If you subtract 17 from my number and multiply the difference by -2, the result is -10." What is the number?
Answer:
22
Step-by-step explanation:
-10/-2 is 5
5+17 is 22
Colton wants to buy a trampoline in 2 months the trampoline costs $228,
if he saves each month how much will he have to save each month?
Answer:
114 each month
Step-by-step explanation:
Answer:
114
Step-by-step explanation:
228 divided by 2 = 114
PLZ HELP find the y and x-intercepts. y=-2x+4 PLEASE EXPLAIN
[tex]\text{Given that,}\\\\y = -2x+4\\\\\text{Plug y= 0 to find the x-intercept,}\\\\0 = -2x +4\\\\\implies 2x = 4\\\\\implies x = \dfrac 42 = 2\\\\\text{So the x - intercept is (2,0)} \\ \\\text{Plug x =0 to find the y-intercept.}\\\\y = -2(0) +4 = 0 +4 = 4\\\\\text{So the y - intercept is (0,4)} \\[/tex]
what is cosec32°/sec58°=
Answer:
1
Step-by-step explanation:
Using the cofunction identity
sec(90 - x) = cosecx , then
sec(90 - 58)° = cosec32° , so
[tex]\frac{cosec32}{sec58}[/tex]
= [tex]\frac{cosec32}{cosec32}[/tex]
= 1
questions
124 - 444 = ...
345 - (-7) × (-6) = ...
Answer:
-320; 303
Step-by-step explanation:
Well... you could really just use a calculator to do this, I mean?
124 - 444 = -320
345 - (-7)*(-6) = 345 - 42 = 303
Answer:
1) 320
2) 303
Step-by-step explanation:
1) simple Subtraction
2) first multiply -7 & -6 = 42
then 345-42 = 303
What is the slope of the line that passes through the points (5, 6)(5,6) and (5, 9) ?(5,9)? Write your answer in simplest form.
Answer:
The slope is undefined.
Step-by-step explanation:
You can use slope formula (y - y)/(x - x) and you will get a zero on the bottom (never allowed) OR notice that the x's are the same so sketch a graph, the line is vertical...that means that slope is undefined.
The image of a point k(-3,4) under a translation 5/2 is
Answer:
try to use automath, it really helps
Evaluate -(2-6)(23).
O A. -8
B.
1/8
C. 8
O D.
- 1 / 8
Answer:
92
Step-by-step explanation:
- ( 2 - 6 )
= - ( - 4 )
= 4
- ( 2 - 6 ) ( 23 )
= 4 x 23
= 92
The evaluation of - (2- 6) ( 23) is 92
In mathematics, evaluation is a systematic method used in solving expressions. From the given information, we need to first solve the expressions in the brackets before multiplying them together.
From the given information:
= - ( 2 - 6) (23)
= - ( -4) (23)
= 4 × 23
= 92
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what is the slope of the line that goes through 11,2 and 14,16
Step-by-step explanation:
m = y2-y1/x2-x1
m = 16 - 2/ 14 - 11
m = 14/3
m = 14 / 3
Hope it helps.
The graph of a function is shown on the coordinate plane below. Identify the rate of
change of the function.
=========================================================
How to get that answer:
The slope is the rate of change for any linear function.
Apply the slope formula for any two points on the diagonal line.
I'll use the points (-4, -3) and (0, 4)
[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{4-(-3)}{0-(-4)}\\\\m = \frac{4+3}{0+4}\\\\m = \frac{7}{4}\\\\[/tex]
The slope is m = 7/4
This indicates that each time we go up 7 (rise), we also go to the right 4 units (run)
slope = rise/run = 7/4
rise = 7, run = 4
The fraction 7/4 converts to the decimal form 1.75
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Find the area of the shape shown below.
Answer:
28 units.
Step-by-step explanation:
Area of square + Area of triangle + Area of rectangle = Area of figure shown
=> (4 x 4) + (1/2 x 4 x 2) + (2 x 4) = Area of figure shown
=> 16 + 4 + 8 = Area of figure shown
=> 28 = Area of figure shown
Therefore, the area of the figure is 28 units.
Hoped this helped.
Answer:
28 units.
Step-by-step explanation:
Act like the shape is just a normal rectangle, because thats easy to do. If it was a full rectangle the length would be 8 and the width would be 4. The formula for finding area of a rectangle is length times width so 8x4 is 32. Now, to find the actual area of the shape, you have to subtract a bit. (I'll add a picture to better explain what I am meaning) You imagine see a mini rectange in the corner with a length of 4 and a width of 2. The area for that is 8. But, only half of that imaginary rectangle is in the actual shape so subtract half of that shape (4) from the original 32 and you get 28. The area is 28 units.
what is the least common denominator of 10 and 14
Answer:
70
Step-by-step explanation:
Given -
the least common denominator of 10 and 14 is - *70*
Prime factor of 14 are 2 and 7
14 = 2 * 7
Prime factor of 10 are 2 * 5
10 = 2 * 5
Now Multiplying the highest exponent prime factor to calculate the LCM of 14 and 10
LCM (10,14) = 2 * 5 * 7
LCM (10,14) = 70
if x and y are positive numbers xy = 96 what is the value of x
The value of x is 96/y where y is not equal to zero.
Given the expression that relates x and y as xy = 96
We are told that x and y are positive numbers. To get the value of x, we will divide both sides by y as shown:
[tex]xy = 96\\\frac{xy}{y} =\frac{96}{y} \\x = \frac{96}{y} \\[/tex]
From the result, we can conclude that the value of x is 96/y where y is not equal to zero.
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80 as the product of it prime factors in ascending order
Answer:
Factors of 80: 1, 2, 4, 8, 10, 20, 40, and 80.
Prime Factorization of 80: 80 = 24 × 5.
Step-by-step explanation:
Answer:
This is true
Step-by-step explanation:
This is true because of the communitive property that makes the numbers you multiply the same product in different orders
!!!!!!!!!!!!!!determine which of these are perpendicular parallel or none
Answer:
Parallel: a and c
Perpendicular: a and b, c and b
Step-by-step explanation:
Basically you would want to isolate for y.
Line a:
4y - 12x = 20
4y = 12x + 20
y = 12x/4 + 20/4
y = 3x + 5
Line b:
3y = -x+2
y = -x/3 + 2/3
Line c:
y=3x - 1
Now look at each line and compare their slopes.
-Lines a and c have same slope., thus they are parallel.
-lines a and b are perpendicular because the slopes are negative reciprocals each other
-lines b and c are also perpendicular
I need answers to these questions
Answer is in the attached file...
Helppppp, please look at the question
Can you Explain your thinking.
Answer:
Record yourself explaining your thoughts and listen to the recording. Continue re-recording what you say and listening to your recording until it sounds they way you want it to.
An amusement park has two themed resorts, Stargazer Suites and Retro Retreat. The graph and table below display the cost of the stay, y, for different numbers of nights, x, for the two different resorts.
Which statement correctly compares the nightly rates at Stargazer Suites and Retro Retreat?
The nightly rate at Stargazer Suites is $15 more than the nightly rate at Retro Retreat.
The nightly rate at Stargazer Suites is $25 more than the nightly rate at Retro Retreat.
The nightly rate at Retro Retreat is $30 more than the nightly rate at Stargazer Suites.
The nightly rate at Retro Retreat is $80 more than the nightly rate at Stargazer Suites.
The nightly rate at each resort is the same.
Answer:
to confusing
Step-by-step explanation:
Answer:
The nightly rate at Stargazer Suites is $25 more than the nightly rate at Retro Retreat.
Step-by-step explanation:
Show Work to factor the binomials.
[tex](14)\\\\x^2 + 14x +45\\\\=x^2 +5x +9x +45\\\\=x(x+5) +9(x+5)\\\\=(x+9)(x+5)\\\\(15)\\\\x^2 +18x +45\\\\=x^2 +15x +3x +45\\\\= x(x+15) +3(x+15)\\\\=(x+3)(x+15)\\\\\\(16)\\\\x^2+46x+45\\\\=x^2 +45x +x +45\\\\=x(x+45) +(x+45)\\\\=(x+45)(x+1)[/tex]
Write an equivalent expression.
1. 8(y - 7)
2. -2x + 7
3. 3/5x + 2/5 + 3/5x
Answer:
8(y - 7) =8y-7-2x+7=7/2=3.5The equivalent expressions are;
1. 8 (y - 7) = 8y - 56
2. - 2 (x + 7) = - 2x - 14
3. 3/5x + 2/5 + 3/5x = (6x + 2) / 5
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expressions are;
1. 8 (y - 7)
2. - 2 (x + 7)
3. 3/5x + 2/5 + 3/5x
Now,
Solve all the expression as;
1. 8 (y - 7) = 8 × y - 8 × 7
= 8y - 56
Thus, 8 (y - 7) = 8y - 56
2. - 2 (x + 7) = - 2 × x - 2 × 7
= - 2x - 14
Thus, - 2 (x + 7) = - 2x - 14
3. 3/5x + 2/5 + 3/5x = 3/5x + 3/5x + 2/5
= (3x + 3x)/ 5 + 2/5
= 6x / 5 + 2/ 5
= (6x + 2) / 5
Thus, 3/5x + 2/5 + 3/5x = (6x + 2) / 5
Therefore, The equivalent expressions are;
1. 8 (y - 7) = 8y - 56
2. - 2 (x + 7) = - 2x - 14
3. 3/5x + 2/5 + 3/5x = (6x + 2) / 5
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Jamaal ran 6 miles in 30 minutes. Which expression shows how to correctly determine his speed in miles per minute?
6 miles ÷ 30 minutes
30 minutes ÷ 6 miles
6 miles ÷ 1 minute
30 minutes ÷ 1 mile
Answer:
The second one. 30 minutes ÷ 6 miles.
Step-by-step explanation:
You want to find how long it took Jamaal to run one mile.
30 minutes ÷ 6 miles = 5 minutes.
So Jamaal can run one mile in 5 minutes.
Option B, 30mins/6miles
if r and s represent the solutions of the equation below and r>s, what is the value of the difference r-s?
(3x+14)x=5
Answer:
16/3
Step-by-step explanation:
(3x + 14)x = 5
3x² + 14x = 5
3x² + 14x - 5 = 0
3x² + 15x - x - 5 = 0
3x(x + 5) - 1(x + 5) = 0
(3x - 1)(x + 5) = 0
x = 1/3 & -5
Here,
r = 1/3
s = -5
r - s
1/3 - (-5)
1/3 + 5
1 + 15/3
16/3
the value of the difference r-s is [tex]\bold{\frac{16}{3}}[/tex]
Answer:
Solution given:
(3x+14)x=5
opening bracket
3x²+14x=5
3x²+14x-5=0
Doing middle term factorisation
3x²+(15-1)x-5=0
3x²+15x-x-5=0
3x(x+5)-1(x+5)=0
(3x-1)(x+5)=0
either
x=-5
or
3x-1=0
3x=1
x=⅓
According to question value of x is r>s
so
⅓>-5
so
r=⅓
and
s=-5
Now
r-s=⅓-(-5)=[tex]\frac{1+5*3}{3}=\frac{16}{3}[/tex]