Please help me and explain to me these questions step by step. Thank youQuestion 8: Use simple interest
Answers
Given:
Amount Nicole borrowed = $1100
Annual interest rate = 7%
Duration = 6 months
Let the amount of interest be x
The amount after t years can be calculated using the formula:
[tex]\text{Amount = }P(1\text{ }+\text{ rt)}[/tex]The interest that she would pay can be calculated using the formula:
[tex]\text{Interest = Amount - Principal}[/tex]The amount after 6 months is:
[tex]\begin{gathered} \text{Amount = 1100(1 + 007 }\times\frac{6}{12}) \\ =\text{ 1138.5} \end{gathered}[/tex]Hence, the interest:
[tex]\begin{gathered} \text{Interest = 1138.5 - 1100} \\ =\text{ 38.5} \end{gathered}[/tex]Answer: $38.5
Related Questions
draw a right triangle with a leg that as a length of 10 and the angle opposite to that side is 55 degrees. find the length of the hypotenuse. round your answer to nearest tenth.
Answers
Question:
Draw a right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees. find the length of the hypotenuse. round your answer to the nearest tenth.
Solution:
A right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees is given by the following picture:
In this case, the appropriate trigonometric identity is:
[tex]\sin (55^{\circ})\text{ = }\frac{y}{h}[/tex]where y is the opposite side, and h is the hypotenuse. Now, replacing the given data in the previous equation we obtain:
[tex]\sin (55^{\circ})\text{ = }\frac{10}{h}[/tex]and solving for h, we get:
[tex]h\text{ = }\frac{10}{\sin (55^{\circ})}\text{ = 12.207}\approx12.21[/tex]then, the correct answer is:
[tex]h\text{ =}12.21[/tex]What is the probability that a randomly selected oar was purchased in the 2010s given that the oar was made from ash wood?Simplify any fractions
Answers
P (A) = probability of a car purchased in 2010's
P (B) = probability of the car being made from ash wood
P (A and B) = 4
P (B) = 4 +3 = 7
Conditional probability:
P (B/A) = P (A and B ) / P (B) = 4 / 7 = 0.5714
A parabola opening up or
equation in vertex form.
down has vertex (-1, 4) and passes through (-2, 17). Write its equation in vertex form.
Answers
Equation of parabola in vertex form is 13x² + 26x + 17
Define Parabola
A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side collide. Ideally, a projectile traveling under the pull of gravity will travel along a curve similar to this one.
Given,
vertex (h,k) = (-1, 4)
points (x,y) = (-2, 17)
We know, The equation in vertex form is
y = a(x - h)² + k
put the (h,k) values,
y = a(x - (-1))² + 4
y = a(x + 1)² + 4 --------- eq(i)
Next, find the value of 'a' by plug in the points of (x, y) in eq(i)
y = a(x + 1)² + 4
⇒17 = a(-2 + 1)² + 4
⇒17 = a(-1)² + 4
⇒17 = a + 4
⇒a = 13
Now, substitute 'a' value in eq(i) to find the equation of parabola
y = a(x + 1)² + 4
⇒ y = 13(x + 1)² + 4
⇒ y = 13(x² + 1 + 2x) + 4
⇒ y = 13x² + 13 + 26x + 4
⇒ y = 13x² + 26x + 17
Therefore, equation of parabola in vertex form is 13x² + 26x + 17
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The population of the state of Colorado was about 5,846,000 people in 2020.
Which number best approximates the population as a single digit times a
power of 10?
OA. 6x 10-6
OB. 6 x 106
C. 5 × 105
D. 5 x 106
Answers
Answer: [tex]6 \times 10^6[/tex] which is choice B
==========================================
Method 1
5,846,000 rounds to 6,000,000 aka "6 million".
This converts to the scientific notation [tex]6 \times 10^6[/tex]
The first 6 is from "6 million", while the 6 as the exponent tells us to move the decimal point that many places to the right to go from 6.0 to 6,000,000
---------------
Method 2
Place a decimal point between the first two digits of 5,846,000 and erase the zeros at the end.
So we get 5.846
We must move the decimal point 6 spaces to the right to go from 5.846 back to 5,846,000 again
Therefore, [tex]5,846,000 = 5.846 \times 10^6[/tex]
Then the 5.846 rounds to 6.0 or simply 6 when rounding to the nearest whole number. This leads to [tex]6 \times 10^6[/tex]
Professor Ivy’s students have a Mean grade of 69.5 and a Standard Deviation of 6.5.3. If Johnny has an 82 in the class, what would the z-score for Johnny’s grade be? (round to the tenthsplace)4. What percentile does Johnny’s score put him in? (round to the nearest whole number)
Answers
Given:
Mean,ц = 69.5
Standard deviation, σ = 6.5
Let's solve for the following:
• 3. If Johnny has an 82 in the class, what would the z-score for Johnny’s grade be?
Apply the z-score formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where:
x = 82
ц = 69.5
σ = 6.5
Thus, we have:
[tex]\begin{gathered} z=\frac{82-69.5}{6.5} \\ \\ z=\frac{12.5}{6.5} \\ \\ x=1.9 \end{gathered}[/tex]Therefore, the z-score is 1.9
Question 4.
Here, we are to find P(Z<1.9).
Using the standard normal distribution table, we have:
NORMSDIST(1.9) = 0.9712
Now convert to percentage:
0.9712 x 100 = 97.12% = 97%
ANSWER:
3). 1.9
4.) 97%
Domain and range from the graph of a piecewise function
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The domain of the given function is:
[tex]\text{Domain}=\lbrack-3,-2\rbrack\cup\lbrack-1,5)[/tex]Because the domain corresponds to the set of all possible inputs, x-axis.
The range of this function is:
[tex]\text{Range}=\lbrack-5,3\rbrack[/tex]Because the range corresponds to the set of all possible outputs, y-axis.
What are inequality? When do we use inequalities?What type of inequalities are there? Which symbols are used for each type?Are the following expressions variable inequalities? Why?a. 13z=27b. x<0c 3x+5x>11d. y+5≤11e. 7-1>- 32
Answers
Inequalities are expressions that refer to non-equivalent quantities. Inequalities can express less than, more than, less than or equal to, more than or equal to.
The type of inequalities and symbols are:
[tex]<,>,\leq,\ge[/tex]So, there are four types of inequalities, for example:
[tex]\begin{gathered} x<2 \\ x>2 \\ x\leq2 \\ x\ge2 \end{gathered}[/tex]Each inequality is different from the other, this means that the symbol used represents a type of inequality.
At last, among the choices, the inequalities are
[tex]\begin{gathered} x<0 \\ 3x+5x>11 \\ y+5\leq11 \\ 7-1>-32 \end{gathered}[/tex]However, variable inequalities mean that the inequalities must have a variable in it. So, they are:
[tex]\begin{gathered} x<0 \\ 3x+5x>11 \\ y+5\leq11 \end{gathered}[/tex]Therefore, the variable inequalities are b, c, and d.
A rock has a mass of 14 g and a volume of 2 cm3. What is the density of the rock? *
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We will determine the density of the rock as follows:
[tex]\rho=\frac{14g}{2cm^3}\Rightarrow\rho=7g/cm^3[/tex]So, the density of the rock is 7 g/cm^3.
Calculate the five-number summary and the IQR from the following values given: {17, 20, 21, 25, 25, 29, 40}
Answers
Answer:
• 17, 20, 25, 29 and 40
,• IQR=9
Explanation:
(a)Given the set of values:
{17, 20, 21, 25, 25, 29, 40}
• The minimum value = 17
The first quartile
The first quartile is the median of the lower half of the data set.
The lower half of the data set = 17, 20, 21
• Therefore, the first quartile =20
The Median
The median is the number in the middle of the set of values.
The number in the middle is 25, therefore:
• Median = 25
The third quartile
The third quartile is the median of the upper half of the data set.
The upper half of the data set = 25, 29, 40
• Therefore, the third quartile =29
Finally, Maximum Value = 40.
The five-number summary of the set of values is: 17, 20, 25, 29 and 40
(b)Interquartile Range
Interquartile Range = Third Quartile - First Quartile
=29 - 20
IQR=9
You are clinic manager. You must schedule the equivalent of 1 1/2 nurses for each doctor on a shift, The friday day shift has 6 doctors scheduled How many nurses you will you need to schedule?
Answers
Data Given:
Nurses = 1 1/2 of each doctor
This can be interpreted as
[tex]\begin{gathered} 1\frac{1}{2}\text{ = }\frac{3}{2} \\ \\ 1\text{ Doctor requires }\frac{3}{2}\text{ times nurses} \end{gathered}[/tex]If there are 6 doctors in the day shift, then there will be
[tex]\frac{3}{2}\text{ x 6 nurs}es[/tex]=>
[tex]\begin{gathered} \frac{3\text{ x 6}}{2} \\ \\ =\text{ 3 x 3 } \\ \\ =\text{ 9 nurses} \end{gathered}[/tex]This means that I will have to schedule 9 nurses for the day shift on Friday
x equals 6 y equals 1 y = x + ?
Answers
The given information is
Kara's original financial plan required that she save $220 amonth for two years in order to have $5,280 for the downpayment on a car. However, after one year she has onlymanaged to save $2,300. How much will Kara have to save each month in the second year in order to reach her original goal of $5,280?
Answers
given data:
the amount needed to pay the downpayment of the car = $5280.
original financial plan = $220 per month.
The amount kara saved after 1 year = $2300.
the balance amount she needed to save
[tex]\begin{gathered} =5280-2300 \\ =2980 \end{gathered}[/tex]now, divide the balance amount by 12, because 1 year =12 months.
[tex]\begin{gathered} =\frac{2980}{12} \\ =248.3 \end{gathered}[/tex]Thus, kara needs to save 248 dollors each month in order to have 5280 dollors after a year.
find the value of expression if d = 10 and c= 5, 5d + c + 2
Answers
the water pressure on Mustafa as he dives is increasing at a rate of 0.992 atmospheres (atm) per meter
What is the rate of increase in water pressure in atm/km
Answers
The rate of increase in water pressure in atm/km = 992 atm/km
what is pressure?Pressure can be defined as the external or internal force that acts on an area of an object which can be measured in atmosphere per meter.
The rate at which Mustafa dives = 0.992atm/meter.
That is,
0.992 atm = 1 meter
X atm = 1 km
But 1000m = 1 km
make X atm the subject of formula;
x atm = 0.992 × 1000
X atm = 992 atm/km
Therefore, the rate in atm/ km would be = 992 atm/km
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In a certain chemical, the ratio of zinc to copper is 4 to 11. A jar of the chemical contains 528 grams of copper. How many grams of zinc does it contain.
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If the ratio of zinc to copper is 4 to 11. A jar of the chemical contains 528 grams of copper. Then 192 grams of zinc does it contain
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that,
In a certain chemical, the ratio of zinc to copper is 4 to 11.
i.e 4:11 or 4 /11
If A jar of the chemical contains 528 grams of copper
We need to find how many grams of zinc does it contain.
Let us consider it as x.
Form a equation,
4/11=x/528
4×528=11x
2112=11x
Divide both sides by 11
192=x
Hence 192 grams of zinc does it contain.
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Find the volume of the cone.9 cmr= 6 cmV = [?] cm3
Answers
The radius of cone is r = 6 cm.
The height of cone is h = 9 cm.
The formula for the volume of cone is,
[tex]V=\frac{1}{3}\pi\cdot r^2\cdot h[/tex]Substitute the values in the formula to determine the volume of cone.
[tex]\begin{gathered} V=\frac{1}{3}\pi\cdot(6)^2\cdot9 \\ =339.29 \\ \approx339.3 \end{gathered}[/tex]Thus, volume of cone is 339.3 cm^3.
Find the area of a regularpolygon with 5 sides that has aside length of 6 inches and anapothem of 9 inches. Area = ?
Answers
SOLUTION
Write out the formula
[tex]\text{area of regular polygon=}\frac{A\text{ }\times P}{2}[/tex]where A= apothem and P= perimeter of the regular polygon
[tex]\begin{gathered} A=9in \\ P=6(5)=30in \\ \text{perimeter of the regular polygon is sum of all the lenght} \\ \text{the number of sides }\times the\text{ lenght of a side } \end{gathered}[/tex]The area of the regular polygon is
[tex]\frac{9\times30}{2}=9\times15=135in^2[/tex]What is the midpoint of the line segment graphed below?10(5,9)(2-1)-1010- 10O A. (7,8)OB.OC (34)OD (710
Answers
ANSWER:
[tex](\frac{7}{2},4)[/tex]STEP-BY-STEP EXPLANATION:
To calculate the value of the midpoint, we use the formula of the midpoint which is the following:
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Replacing and solving the midpoint:
[tex]\begin{gathered} (x_m,y_m)=(\frac{5+2_{}}{2},\frac{9-1_{}}{2}) \\ (x_m,y_m)=(\frac{7_{}}{2},\frac{8_{}}{2})=(\frac{7}{2},4) \end{gathered}[/tex]Question 19 of 25 Which of these is a factor in this expression? 6z^4 - 4+9 (y² +9) O A. (y +9 O B. 624 - 4 OC. 9 (y +9 OD. -4+9 (y +9)
Answers
1) In this expression, we have already a factored form. So the factor in this expression is 9(y³+9) Because multiplying "distributing it" we'll have the whole expression
6z^4 -4+9(y³+9)
6z^4 -4 +9y³+81
2) 9(y³+9)
Jocelyn graphs a linear function that passes through three distinct points: A, B, and C. The coordinates ofpoint A (-3, -3) and point C (3,5) are shown.What are the possible coordinates of point B for Jocelyn’s linear function?
Answers
(0,1) is a possible coordinite through the points (-3,-3), (3,5)
About how many points did the four students score in round 1. Estimate by rounding each point total to the nearest whole number
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The total points that the four students score in round 1 is 75 points.
How to calculate the value?Based on the information given, it's important to convert the numbers to while numbers and then add.
John has 19.5. This will be 20.
Adam had 21.2. This will be 21.
Peter has 23.8. This will be 24.
Grace has 10.2. This will be 10.
The total points will be:
= 20 + 21 + 24 + 10
= 75
The complete question is given below.
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The points of four students are:
John 19.5
Adam 21.2
Peter 23.8
Grace 10.2
About how many points did the four students score in round 1. Estimate by rounding each point total to the nearest whole number
A runner has a track lap time of 3 minutes while at a run, 5 minutes while at a jog, and 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/2 at a jog, and 1/10 at a walk, what is the total track lap time of the runner? Write the solution as a mixed number or a fraction in lowest terms.
Answers
The total track lap time of the runner is 4 11/15 and it has been written as a mixed number or a fraction in lowest terms.
Mixed fraction:
The fraction represented with its quotient and remainder is known as mixed fraction.
Given,
A runner has a track lap time of 3 minutes while at a run, 5 minutes while at a jog, and 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/2 at a jog, and 1/10 at a walk.
Here we need to find the total track lap time of the runner.
Here we can compute the Total Lap Time by multiplying each fraction by its associated lap time, then we get,
Run Lap Time = (2/5)(3) = 6/5 minutes
Jog Lap Time = (1/3)(5) = 5/3 minutes
Walk Lap Time = (4/15)(7) = 28/15 minutes
So, the total lap time is, written as,
Total Lap Time = 6/5 + 5/3 + 28/15
Now, we have to make the fraction equal to each other,
=> (6x3)/(5x3) + (5x5)/(3x5) + (28 x 1)(15 x1)
=> 18/15 + 25/15 + 28/15
=> (18 + 25 + 28)/15 = 71/15
Now, we have to convert this into mixed fraction then we get,
=> 71/15 = 4 11/15
Therefore, the total Lap Time is 4 11/15 minutes.
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answer step by step please suppose AC is congruent with AD. what information would you need to conclude that ADB is congruent with ACE using ASA theorem?
Answers
Answer:
Angle ABD must be congruent to Angle AEC.
Explanation:
Angle: Triangles ADB and ACE share angle A in common.
Side: AD is congruent to AC.
For Triangles ADB and ACE to be congruent by the ASA Congruence Theorem, then the following must hold:
Angle: Angle ABD must be congruent to Angle AEC.
A bucket can hold 26 litres of water when it is 8/9 full. How many litres can it hold when it is full?
Answers
Answer:
[tex]29.25\text{ liters}[/tex]Explanation:
Here, we want to know the amount of water the bucket can hold when full
Let us have the volume as x liters
Mathematically:
[tex]\begin{gathered} \frac{8}{9}\times x\text{ = 26} \\ \\ 8x\text{ = 9 }\times\text{ 26} \\ x=\text{ }\frac{9\times26}{8} \\ \\ x\text{ = 29.25 liters} \end{gathered}[/tex]Triangle XYZ is rotated 90° counterclockwise about the origin.The result is Triangle X'Y'Z', as shown below.
Answers
A shortcut for a 90° counterclockwise rotation:
• If the point (h, k) is rotated 90° counterclockwise rotation, then the final point will be (-k, h).
Answer:
Therefore the coordinates would be:
• X,(-5, 3) → ,X',(-3, -5)
,• Y,(-1, 1) → ,Y',(-1, -1)
,• Z,(-8, -4) → ,Z',(4, -8)
Then, the rule is (x, y) → (-y, x).
Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students. How many students chose not to take French their freshman year?
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Answer:
There were 378 students who chose to study French their freshman year. This means that 72% of the total number of students chose to study French their freshman year. Therefore, the total number of students must be 378 / 0.72 = 527.5. This means that there were 148.5 students who chose not to take French their freshman year.
Step-by-step explanation:
If A is the image of A(3, 4) after a dilation with scale factor 7 about the origin, what is the distance between A and A? Hint: Use the distance formula: d = √√(x₂ − x₂)² + (Y₂ − 3₂)² .
0 7 units
○28 units
O 30 units
O 35 units
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Answer:
Step-by-step explanation:
you can view this,its similar just the numbers are switched.
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Answer:
35
Step-by-step explanation:
sorry if im wrong sorry
Using the image, identify the opposite rays (choose all that apply).
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Solution
The answer is
im confused on what 43/25 as a percent would be
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1------------------------------------>100%
43/25----------------------------->x%
So, using cross multiplication:
[tex]\begin{gathered} \frac{1}{\frac{43}{25}}=\frac{100}{x} \\ \text{solve for x:} \\ x=100\times(\frac{43}{25}) \\ x=172 \end{gathered}[/tex]eln(x-3) = 9what are the steps to solve? I am so confused, what is ln even??