Carol should refinance is D. Yes; the new blended interest rate is lower than the old interest rate.
First, let's understand the 80/20 mortgage breakdown:
80% of the mortgage at 4.5% interest20% of the mortgage at 9.5% interestNext, we calculate the blended interest rate for the new mortgage:
[tex]\text{Blended Rate} = (0.80 \times 4.5\%) + (0.20 \times 9.5\%)[/tex]
a. Calculate each part:
[tex]0.80 \times 4.5\% = 3.6\%[/tex][tex]0.20 \times 9.5\% = 1.9\%[/tex]b. Add these results to get the blended rate:
[tex]3.6\% + 1.9\% = 5.5\%[/tex]
So, the blended interest rate for the new mortgage is 5.5%.
Now, compare this with Carol's current fixed-rate mortgage interest rate of 6.25%:
Current interest rate: 6.25%New blended interest rate: 5.5%The new blended interest rate (5.5%) is lower than the old interest rate (6.25%). Therefore, based on the interest rates alone, Carol should refinance.
a penny is dropped from the top of the building and takes 9 seconds to fall to the ground. What is the height of the building D=distance T=Time
The height of the building is 9x.
What is Distance- time formula?Speed is a measure of how quickly an object moves from one place to another. It is equal to the distance traveled divided by the time.
Given:
Time= 9s
Let the speed of penny be 'x'.
We know,
speed = distance / time
distance = speed* time
distance = x *9
distance = 9x.
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I don’t know how to do the work I just don’t understand
Answer:
1. is -5/7
2. is 6/-9 OR 1/-3 (negative one third)
3. is 2
Step-by-step explanation:
Arrange the numbers 2,3,4,5,6,7,8,9 and 10 in the accompanying triangle so that each side sums to 21 show your answer and please help
All three sides will be equal to 21.
So that is
3 + 7 + 9 + 2 = 21,
3 + 8 + 6 + 4 = 21 and
2 + 10 + 5 + 4 = 21
What are Arithmetic operations?Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.
The operator that performs the arithmetic operations are called arithmetic operators.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
Given
Put the Number from 2 to 10 in the circle so that the sum of the Number on each side of a triangle is the same.
3
7 8
9 6
2 10 5 4
So the numbers form a triangle and assume that a circle is drawn on the numbers.
If we add the numbers all the three sides will be equal to 21.
So that is
3 + 7 + 9 + 2 = 21,
3 + 8 + 6 + 4 = 21 and
2 + 10 + 5 + 4 = 21
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Georgia participated in a sleep study in which scientists found that she fell into REM sleep exactly every 45 minutes while she
was asleep. If Georgia was asleep for 6 hours (390 minutes), how many periods of REM sleep did she have?
The number of periods of REM sleep Georgia has in the 6 hours (390 minutes) as stated in the question is 8.667 periods.
Using the standard time conversion, the number of periods is 8 hours.
How do we determine the number of periods Georgia falls into in REM sleep using word problems.To determine the number of periods of REM sleep that Georgia has, we need to divide the total number of minutes of sleep by the interval at which she falls into the REM sleep.
From the given information:
Georgia was asleep for = 390 minutesNumber of intervals she falls into REM = every 45 minutesThe number of periods of REM sleep she has in 390 minutes of sleep is:
= 390 minutes/ 45 minutes
= 8.667 periods.
NOTE: We have only 360 minutes in 6 hours since 60 minutes = 1 hour.
= 360 minutes/ 45 minutes = 8 periods.
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What is the area of triangle IHC?
Answer:
[tex]28 cm^2[/tex]
Step-by-step explanation:
The formula for finding the area of a triangle is:
[tex]\frac{1}{2} bh[/tex]
The "b," is the base (7), and the "h," is the height (8):
[tex]\frac{1}{2} (7)(8)[/tex]
[tex]\frac{1}{2} (56)[/tex]
28
"The area of triangle [tex]IHC is $\boxed{\frac{1}{2} \times b \times h}$[/tex], where [tex]$b$[/tex] is the base of the triangle and[tex]$h$[/tex]is the height of the triangle.
To determine the area of triangle IHC, we need to know the lengths of the base and the height. The area of a triangle is given by the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
In the case of triangle IHC, if we let b represent the length of the base IH, and h represent the length of the height from point H to side IH, then the area of triangle IHC can be calculated using these values.
Without specific numerical values for b and h, we cannot calculate a numerical area. However, if the values of b and h are provided, we can substitute them into the formula to find the area. For example, if b = 6 units and h = 4 units, then the area would be:
[tex]\[ \text{Area} = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \][/tex]
Thus, the area of triangle IHC with a base of 6 units and a height of 4 units would be 12 square units. If the actual lengths of the base and height are different, those values should be substituted into the formula to calculate the correct area."
You use the associative property of multiplication to change how factors
are grouped. In the example, why are the factors of the term 3 x 7a
regrouped as (3 x 7)a?
Your answer
Answer:3x7
Step-by-step explanation:
Okay so I don’t think I can get it to you tomorrow or tomorrow if you want to know if you want
the factors of the term [tex]3 \times (7a)[/tex] are regrouped as [tex](3 \times 7) \times a[/tex] so that by using the associative property we can simplify the multiplication process and ensure consistency in mathematical calculations.
The associative property of multiplication states that the way in which factors are grouped in a multiplication problem does not change the product. This property can be written mathematically as:
[tex](a \times b) \times c = a \times (b \times c)[/tex].
In the example, the factors 3 and 7a are initially grouped as [tex]3 \times (7a)[/tex]. Using the associative property, we regroup them as [tex](3 \times 7) \times a[/tex]. This shows that it doesn't matter how we group the numbers; the product will be the same.
For instance:
[tex]3 \times 7a = (3 \times 7) \times a = 21a[/tex]
This regrouping can make calculations simpler because it allows us to first multiply 3 and 7 to get 21 and then multiply by the variable a, rather than working directly with the expression 7a.
In the example, the factors of the term [tex]3 \times (7a)[/tex] are regrouped as [tex](3 \times 7) \times a[/tex] so that by using the associative property we can simplify the multiplication process and ensure consistency in mathematical calculations.
Given: PRST square
PMKD is a square
PR = a, PD = a
Find the area of PMCT.
PLEASE HELPP
Answer:
7a²/16
Step-by-step explanation:
Area of the triangle PTS
½ × a × a
a²/2
Length of PS:
sqrt(a² + a²)
asqrt(2)
Length of MS:
¼asqrt(2)
Triangles MCS and TPS are similar
With sides in the ratio:
¼asqrt(2) : a
sqrt(2)/4 : 1
Area of triangle SMC:
A/(a²/2) = [(sqrt(2)/4)]²
2A/a² = 1/8
A = a²/16
Area of PTMC
= a²/2 - a²/16
= 7a²/16
Step-by-step explanation:
This is a much more interesting problem than what we usually see here.
Let's just start by assuming a=1 so we have two unit squares.
PMC and PTC are two congruent triangles, each right triangles with one leg of length 1 and a shared hypotenuse PC.
We'll put it on the grid at P(0,0), T(1,0).
Angle TPM is 45 degrees and PM=1 so
M(cos 45, sin 45) = M(1/√2, 1/√2)
MK has slope -1, thru M, so is
y = -x + √2
C's on that line at x=1, so C's x coordinate is 1, so its y coordinate is √2 - 1
C(1, √2 - 1)
OK, that's enough to compute the area.
P(0,0), T(1,0), C(1, √2 - 1), M(1/√2, 1/√2)
area(PMCT) = area(PTC) + area(PCM)= 2 area(PTC)
The area of a right triangle is half the product of its legs.
area(PMCT) = 2 (1/2) (1) ( √2 - 1)
area(PMCT) = √2 - 1
When we have sides a, the area scales by a²,
Answer: a²(√2 - 1)
evaluate the expression for q=8
7q
Answer:
The answer is 56.
Step-by-step explanation:
7 * 8 = 56
what is the volume of a cylinder with a radius of 3 and a hight of 6?
Answer:
Around 169.65.
Step-by-step explanation:
The formula is (pi)r^2*h
(pi)3^2*6
(pi)9*6
54(pi)
169.65
Which function, gor h, is the inverse function for function f?
A. the function gbecause the graphs of fand gare
symmetrical about the line y= x
CB. the function g because the graphs of fand gare
symmetrical about the x-axis
C. the function h because the graphs of fand hare
symmetrical about the line y= x
D. the function h because the graphs of fand hare
symmetrical about the x-axis
For a biology assignment, Josephine records the height of a plant over
time. The plant was 12 cm tall when she started the assignment. She
notices that the plant grows 2 cm every week,
What point is on her graph ?
Answer:
3,18
Step-by-step explanation:
can anyone help me with this question??
Answer:
The answer is B
Step-by-step explanation:
You don't need elimination for this when you plug it in 10(-5) is equal to -50 add 5 to that to get -45
and -5(2)=-10 +5 to get -5 showing that b works
Scott has a container of ping pong balls and golf balls. The number of ping pong balls in the container is 8 times as many as the number of golf balls in the container. If there are 10 golf balls in the container, how many ping pong balls are in the container?
a.88
b.80
c.2
d.18
Answer:
b)
Step-by-step explanation:
Number of ping pong balls = 8 * number of golf balls
= 8*10
= 80
What is the discriminant of the quadratic equation 9x2 – X – 8=0?
Answer:
288
Step-by-step explanation:
a = 9
b = -1
c = -8
b^2 * -4 * ( a * c )
Just filing in the numbers given above:
-1^2 * -4 * ( 9 * -8 )
1 * -4 * ( -72)
1 * + 288 = 288
Ataut telephone wire extends from the top of a 40-foot tall telephone pole to a stake in the
ground 9 feet away. A bug crawled from the stake in the ground up the wire to the top of the
telephone pole. Then the bug crawled down to the bottom of the pole and back to the stake. How
far did the bug crawl?
feet
The bug crawl in total of 90 feet of distance .
What is right angle triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle or two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry.
According to question
Ataut telephone wire extends from the top of a 40-foot tall telephone pole to a stake in the ground 9 feet away
So, according to diagram
AB= 9 feet
AC = 40 feet
BC =[tex]\sqrt{AB^{2} +AC^{2} }[/tex](Pythagoras theorem)
BC = [tex]\sqrt{9^{2} +40^{2} }[/tex]
BC=[tex]\sqrt{81 + 1600 }[/tex]
BC = [tex]\sqrt{ 1681 }[/tex]
BC= 41 feet
As bug start from the stake in the ground up the wire to the top of the
telephone pole. Then the bug crawled down to the bottom of the pole and back to the stake which means perimeter of right angle triangle.
Perimeter of triangle = AB + BC + AC
= 9 + 41 + 40
= 90 feet
Hence, the total distance travelled by bug is 90 feet .
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1. 4 and 4
Find the geometric mean between each pair of numbers
Answer:
2
Step-by-step explanation:
i think bc its on the middle but its ben a min since ive done it
Look at the attached screen shot. The population is 2 while the geometric mean is (Xg):4
The quadratic equation 4x2 + 45x + 24 = 0 was solved using the Quadratic Formula, x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a.
One solution is −10.69. What is the other solution? Round to the hundredths place.
0.51
10.69
−1.12
−0.56
Answer:
The other solution is -0.56
Step-by-step explanation:
Quadratic equation :[tex]4x^2 + 45x + 24 = 0[/tex]
General quadratic equation : [tex]ax^2+bx+c=0[/tex]
Om comparing :
a=4
b = 45
c=24
Formula : [tex]x =\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
Substitute the values in the formula :
[tex]x=\frac{-45 \pm \sqrt{45^2-4(4)(24)}}{2(4)}\\x=\frac{-45 + \sqrt{45^2-4(4)(24)}}{2(4)},\frac{-45 - \sqrt{45^2-4(4)(24)}}{2(4)}\\x=-0.5613,-10.688[/tex]
So, One solution is −10.69.
So, Other solution is −0.56
Hence the other solution is -0.56
The second solution to this equation is −0.56.
Explanation:In the given quadratic equation 4x2 + 45x + 24 = 0, the quadratic formula is used to find the solutions, or roots, of the equation.
This formula is x = [-b ± sqrt(b² - 4ac)] / (2a).
For this specific equation, a is 4, b is 45, and c is 24.
Since it's already given that one root is -10.69, the other root should be obtained by substituting the values into the formula and choosing the alternative sign:
x = [-45 - sqrt(45² - 4*4*24)] / (2*4) this calculation would give −0.56, which is the other solution to the equation.
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so 5(4d+8) = 40 so what does d= ?
Answer:
d = 0.
Step-by-step explanation:
First, use the distributive property and distribute the 5.
The equation is now 20d + 40 = 40.
Subtract 40 from both sides to isolate the variable.
The equation is now 20d = 0.
Now you're thinking, this can't be possible! But really, 0 / 20 is possible. The answer is d = 0.
What is the average speed of a cheetah that runs 9 km in 10 minutes? Give your answer in km/hr. (Hint: 10 minutes is 1/6 of an hour.)
Answer:
54kph
Step-by-step explanation:
A small bar of gold measures 40mm by 25mm by 2mm. One cubic millimeter of gold weighs about 0.0005 ounce. Find the voulme in cubic millimeters and the weight ounces of the small bar of gold.
Answer:
Look below for answer!
Step-by-step explanation:
Hope this Helps!!!
⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇
Can someone answers this please
Answer:
y = - 24
Step-by-step explanation:
[tex]y = (x - 4)(x + 6) \\ plug \: x = 0 \\ y = (0 - 4)(0 + 6) \\ y = ( - 4)(6) \\ y = - 24 \\ \purple{ \bold{ \therefore \: y - intercept = - 24}}[/tex]
Please help with this! :)
Answer:
4 and 3 <------- That's the set I believe!
Mrs. Williams estimates that on average her family recycles 12.6 pounds of plastic each month. In a year's time, how much landfill space will Mrs. William's family save if 1 pound of plastic saves 7.4 yards of landfill space?
a.
932.40 yards
b.
93.24 yards
c.
1,118.88 yards
d.
7.77 yards
Answer:B
Step-by-step explanation:
Mrs. Williams' family recycles 151.2 pounds of plastic in a year, and since 1 pound of plastic saves 7.4 yards of landfill space, their recycling efforts save approximately 1,118.88 yards of landfill space annually.
Explanation:To find out how much landfill space Mrs. Williams family can save in a year, we can start by calculating how much plastic they recycle in a year. This can be done by multiplying the monthly amount by the total number of months:
12.6 (pounds per month) x 12 (months per year) = 151.2 pounds of plastic
Next, we use the fact that every pound of plastic recycled saves 7.4 yards of landfill space. So, we multiply the total pounds of plastic by the amount of space saved per pound:
151.2 (pounds of plastic) x 7.4 (yards per pound) = 1,118.88 yards
Therefore, Mrs. Williams family can save approximately 1,118.88 yards of landfill space per year by their recycling efforts.
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GIVING BRAINLIEST ..Can somebody help me (explain your answer)
Answer:
13.04 units to the nearest hundredth.
Step-by-step explanation:
Use the Pythagoras theorem:
c^2 = a^2 + b^2 where a, b and c are the sides of a right triangle with c the hypotenuse.
In our triangle ( x = length of the hypotenuse):
x^2 = 13^2 + 1^2
x^2 = 169 + 1 = 170
x = √170
= 13.04.
If we are doing this mentally the best we can do is say that the hypotenuse is a small amount greater than 13.
If a figure has 90° rotational symmetry, what other symmetries must it have?
Answer:
Step-by-step explanation:
The figure must also have the rotational symmetry of 180/270°.
What are symmetries in math?
In geometry, symmetry is defined as a balanced and proportionate similarity that is found in two halves of an object. It means one-half is the mirror image of the other half. The imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry.
What are the four types of symmetries?Types of symmetries are rotational symmetry, reflection symmetry, translation symmetry, and glide reflection symmetry. These four types of symmetries are examples of different types of symmetry on a flat surface called planar symmetry.
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ABC bookstore sells packages of books that include both new and used books. New books cost $18 and used books cost $9. The bookstore wants to sell packages that have 36 books total, and the store charges $432 for each package. How many new and used books will each be in the package?
Answer:12 new, 24 used
Step-by-step explanation: i think this is right, sorry if not.
12 x 18= 216
9 x 24 = 216
216 + 216 = 432
HELP i need help with this!!!
Answer:
A=26.75
Step-by-step explanation:
A=1/2(2)(2)=2
A=1/2(5)(2)=5
A=1/2(2+2+5)(3.5)=15.75
A=2+5+15.75=26.75
Omg 1+1 totally doesn’t even 2
Lemme stop acting slow
The numbers 1 through 10 are put in one bag. The numbers 5 through 14 are put in another bag. When you pick one number from each bag, what is the probability you get the same number?
Answer:
0.06 or 6%
Step-by-step explanation:
Both bags have the numbers 5, 6, 7, 8, 9 and 10. Thus, there are 6 similar number in both bags.
The probability of picking the number 5 in both bags is:
P(5)= 1/10 * 1/10= 1/ 100
It is the same probability of picking the number 6 or 7 or 8 or 9 or 10 in both bags.
P ( 6)= 1/100
P ( 7 ) = 1 /100
P (8)= 1 /100
P ( 9 ) = 1 /100
P ( 10 ) = 1 /100
Gwen is a makeup artist and carries a lot of makeup around with her. She has 8 cosmetics in her bag, including 2 lip glosses.
What is the probability that a randomly selected makeup item from her bag will be a lip gloss?
!!!Write your answer as a fraction or whole number!!!
Answer:
2% hope it helpssss
Step-by-step explanation:
Answer:
2/8 or 1/4
Step-by-step explanation:
So pretty much you just turn the number into a fraction