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i need help now plsssss
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If value of a₁=1 and equation is aₙ= -5aₙ₋1 then value of a₆ is -3125
If a₁=1 and equation aₙ= -5aₙ₋1
a₁= -5a₀
a₂= -5a₁
a₂= -5
a₃= -5a₂ = -5(-5)= 25
a₄=-5a₃ = -5(25) =-125
a₅=-5a₄ = -5(-125)=625
Value of a₆=-5a₅ = -5(625)=-3125
Hence, if value of a₁=1 and aₙ= -5aₙ₋1 then value of a₆ is -3125
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2 boxes shown are cuboids. The bigger cuboid has a length of 50 cm, a width of 30 cm, and a height of 20 cm. The smaller cuboid has a length of 10 cm, a width of 3 cm, and a height of 4 cm. How many smaller boxes would you need to fill up the bigger box entirely?
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Answer:
To calculate the number of smaller boxes that would fill up the bigger box entirely, we need to divide the volume of the bigger box by the volume of the smaller box.
The volume of the bigger box is:
Volume = length x width x height
Volume = 50 cm x 30 cm x 20 cm
Volume = 30,000 cm³
The volume of the smaller box is:
Volume = length x width x height
Volume = 10 cm x 3 cm x 4 cm
Volume = 120 cm³
Now we can divide the volume of the bigger box by the volume of the smaller box to get the number of smaller boxes that would fill up the bigger box:
Number of smaller boxes = Volume of bigger box / Volume of smaller box
Number of smaller boxes = 30,000 cm³ / 120 cm³
Number of smaller boxes = 250
Therefore, we would need 250 smaller boxes to fill up the bigger box entirely.
The two lines below are parallel if the slope of the red line is 5 what is the slope of the green line
Need help fast
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Since the two lines above are parallel, if the slope of the red line is 5, then the slope of the green line is equal to 5.
What are parallel lines?In Mathematics and Geometry, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
In Mathematics and Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂
This ultimately implies that, the slope of these two lines are equal and the same, and as such, we have the following:
Slope of red line = Slope of green line
5 = 5
In conclusion, we can reasonably infer and logically deduce that the slope of the green line is equal to 5.
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Find the length of the third side. If necessary, round to the nearest tenth.
15
9
Answers
To find a missing side of a right triangle, you will use the Pythagorean theorem:
a^2 + b^2 = c^2
a and b are the legs and c is the hypotenuse.
The information given is not enough to solve this problem, but I will assume the hypotenuse is 15 and one of the legs is 9.
So:
9^2 + b^2 = 15^2
Calculate:
81 + b^2 = 225
Subtract 81 to both sides:
b^2 = 144
Square root both sides:
b = 12
The length of the third side is 12.
***This is only an assumption as to what the problem is. If it is Pythagorean theorem, check to see if the assumed sides are correct, if not, switch the numbers.
Hope this helped!
On the decibel scale, a sound that is 10 decibels higher is 10 times as loud. That means a sound that is twenty decibels higher is 100 times as loud. How many more times louder than a 40-dB conversation is a 120-dB jet plane taking off? Explain your thinking.
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The jet plane taking off is 100 million / 1 million = 100 times louder than the conversation.
According to the decibel scale, a sound that is 10 decibels higher is 10 times as loud. Therefore, a sound that is 20 decibels higher is 10 times 10, or 100 times as loud. This means that a 120-dB jet plane taking off is 100 times as loud as a sound that is 20 decibels lower, which is a 40-dB conversation.
To find out how many more times louder a 120-dB jet plane taking off is than a 40-dB conversation, we can divide the loudness of the jet plane by the loudness of the conversation
120 dB / 40 dB = 3
This means that a 120-dB jet plane taking off is 3 times as loud as a 40-dB conversation. However, we need to remember that the decibel scale is logarithmic, which means that each increase of 10 decibels represents a tenfold increase in loudness. Therefore, a 30-dB increase represents a thousandfold increase in loudness (10 to the power of 3).
Since the difference between 120 dB and 40 dB is 80 dB, which is 8 times 10 dB, the loudness of the jet plane taking off is 10 to the power of 8, or 100 million, times as loud as the conversation.
Therefore, the jet plane taking off is 100 million / 1 million = 100 times louder than the conversation.
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Question content area top Part 1 On a certain hot summer's day, 574 people used the public swimming pool. The daily prices are $1.75 for children and $2.25 for adults. The receipts for admission totaled $1180.00. How many children and how many adults swam at the public pool that day?
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The number of children and the adults present at the pool in the day was 223 and 351 respectively.
Given that, there are 574 people in a day swimming at public pool, the daily prices are $1.75 for children and $2.25 for adults.
The receipts for admission totaled $1180.00.
Let the number of adults be a and that the children be c,
So,
a + c = 574
a = 574 - c.........(i)
2.25a + 1.75c = 1180............(ii)
Put eq(i) in eq(ii)
2.25(574-c) + 1.75c = 1180
1291.5 - 2.25c + 1.75c = 1180
0.5c = 111.5
c = 223
Put the value of c in the eq(i)
a = 574-223
a = 351
Hence, the number of children and the adults present at the pool in the day was 223 and 351 respectively.
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a traffic light is red for 60 seconds, yellow for 10 seconds, and green for 90 seconds. assuming that arrival times at the light are uniformly distributed, what is the probability a car stops at the light for more than 30 seconds?
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The probability that a car stops at the light for more than 30 seconds is approximately 0.714, or 71.4%.
To calculate the probability that a car stops at the light for more than 30 seconds, we need to first calculate the total time of the traffic light cycle, which is:
60 seconds (red) + 10 seconds (yellow) + 90 seconds (green) = 160 seconds
Next, we need to calculate the probability that a car arrives at the traffic light during each color phase. Since arrival times are uniformly distributed, the probability of a car arriving during any particular phase is simply the duration of that phase divided by the total cycle time. Therefore:
- Probability of arriving during red phase = 60/160 = 0.375
- Probability of arriving during yellow phase = 10/160 = 0.0625
- Probability of arriving during green phase = 90/160 = 0.5625
Now, to calculate the probability that a car stops at the light for more than 30 seconds, we need to consider two cases:
1. The car arrives during the red or yellow phase: In this case, the car will stop at the light for at least 60 seconds (the duration of the red phase) before the light turns green. Therefore, the probability of stopping for more than time 30 seconds in this case is:
Probability of arriving during red phase * Probability of stopping for more than 30 seconds during red phase = 0.375 * (60-30)/60 = 0.25
Probability of arriving during yellow phase * Probability of stopping for more than 30 seconds during yellow phase = 0.0625 * (90-30)/90 = 0.375
Total probability for this case = 0.25 + 0.375 = 0.625
2. The car arrives during the green phase: In this case, the car will not stop at the light if it arrives before the end of the green phase, which happens with probability:
Probability of arriving during green phase * Probability of arriving before end of green phase = 0.5625 * 90/160 = 0.315625
Therefore, the probability of stopping for more than 30 seconds in this case is:
Probability of arriving during green phase * Probability of stopping for more than 30 seconds during green phase = 0.5625 * 0.5 = 0.28125
Total probability for this case = 0.315625 * 0.28125 = 0.0888671875
Finally, we can add the probabilities from both cases to get the total probability of stopping for more than 30 seconds:
Total probability = Probability from case 1 + Probability from case 2 = 0.625 + 0.0888671875 = 0.7138671875
Therefore, the probability that a car stops at the light for more than 30 seconds is approximately 0.714, or 71.4%.
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what is the slope of (6,545) and (4,225)
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The slope of the line that passes through the points (6, 545) and (4, 225) is equal to 160.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the slope formula, we have the following;
Slope (m) = (225 - 545)/(4 - 6)
Slope (m) = -320/-2
Slope (m) = 160.
Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 160.
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The table of values represents a
quadratic function.
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Answer:
f(x) = x² +4x -12
Step-by-step explanation:
You want the standard form equation of the quadratic represented by the values in the table.
MinimumThe table shows the minimum is -16 at x = -2. That is, the vertex is at (-2, -16).
The table also shows the function value increases by 1 to -15 when x is ±1 unit from its vertex value. That increase of 1 tells you the leading coefficient is 1.
Vertex formThe vertex form of a quadratic equation is ...
f(x) = a(x -h)² +k
where 'a' is the leading coefficient, and (h, k) is the vertex.
For this function, we have a=1, (h, k) = (-2, -16), so the vertex form of the equation is ...
f(x) = (x +2)² -16
Standard formExpanding the vertex form equation, we get ...
f(x) = (x² +4x +4) -16
f(x) = x² +4x -12
Isaiah made the model to show multiplying a fraction by a fraction. Which multiplication sentence does the model
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Isaiah multiplied 3.92 and 47.6 together, with a result of 186.592 is correct, option D is correct.
To multiply decimals, we need to ignore the decimal point initially and treat the numbers as whole numbers.
We then multiply the numbers as usual and count the total number of decimal places in the numbers being multiplied.
We place the decimal point in the answer by counting the same number of decimal places from the right-hand side of the product.
In this case, if we ignore the decimal point initially and treat 3.92 and 47.6 as whole numbers, we get:
392 × 476 = 186,592
We then count the total number of decimal places in the numbers being multiplied, which is two (one from 3.92 and one from 47.6).
We place the decimal point in the answer by counting two decimal places from the right-hand side of the product, which gives us:
3.92 × 47.6 = 186.592
Therefore, Isaiah's result of 186.592 is correct.
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Isaiah multiplied 3.92 and 47.6 together, with a result of 186.592. Which of the following statements is true?
Isaiah's result is incorrect. He place the decimal point in the wrong place.
Isaiah's result is incorrect. He made a mistake when adding the partial products together.
Isaiah's result is incorrect. He made a mistake in multiplying.
Isaiah's result is correct.
The diameter of a circular track is 400 meters. If you ran around the track twice, how far did you travel in total?
Answers
Answer:800 Meters
Step-by-step explanation:
400X2= 800
What is the value of x? Responses 4 4 43√ 4 square root 3 8 8 83√
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Using trigonometric functions, note that the value of x, in this case, is 4√3. See the explanation below.
How is this so?We can use trig functions since this is a right triangle
The side opposite the right angle is 8, that is the hypotenuse
We know the opposite side is x
sin theta = opp/ hyp
sin 60 = x/8
Multiply each side by 8
8 sin 60 =x
sin 60 = √(3)/2
8√3/2 =x
4 √3 =x
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Full Question:
What is the value of x?
a: 4
b: 43√
c: 8
d: 83√
The figure contains a right triangle. The side opposite the right angle is 8. The side opposite the 60 degree angle is x.
See attached image.
what is 5 rounded to the nearst thenth
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Answer:
5 is rounded to 5.0
Step-by-step explanation:
Whats the slope of the line
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Explanation:
(-4,8) simplified divided by 4 on both sides is (-1/2)
Acellus - geometry (thank you)
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The perimeter of the given polygon is 32 cm.
What is the perimeter?Perimeter is the sum of the length of the sides used to make the given figure.
In the given figure, name the points given as E, F, G, and H. The naming of the points is shown in the image below.
Now, the two-tangent theorem states that if two tangents of the circle are drawn such that the tangents intersect each other at a point outside the circle then the tangents will be congruent to each other.
As per the theorem,
AE ≅ AH; AE = AH = 3 cm
BH ≅ BG; BH = BG = 4 cm
CF ≅ CG; CF = CG= 5 cm
Also, since∠B ≅ ∠D,
BG = BH = DE = DF = 4 cm
Therefore, the perimeter of the given figure is,
Perimeter = AE+DE+DF+CF+CG+BG+BH+AH
= 3 cm + 4 cm + 4 cm + 5 cm + 5 cm + 4 cm + 4 cm + 3 cm
= 32 cm
Hence, the perimeter is 32 cm.
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Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1
an = n
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Answer:
The sequence defined by an = n for n ≥ 1 can be written as:
a1 = 1
a2 = 2
a3 = 3
a4 = 4
Therefore, the first four terms of the sequence are 1, 2, 3, and 4.
Determine la distancia en tree los puntos (-3,1)y (3,5)
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The distance between the given points is equals to 7.21 units ( approximately).
Coordinates of the two points are.
( x₁ , y₁ ) = ( -3, 1 )
( x₂ , y₂ ) = ( 3, 5 )
The distance formula to find the distance between the points (-3,1) and (3,5) is equal to ,
Distance 'd' = √( y₂ - y₁ )² + ( x₂ - x₁ )²
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
And d is the distance between them.
Substitute the coordinates of the given points, we have,
⇒ Distance 'd'= √((3 - (-3))²+ (5 - 1)²)
⇒ Distance 'd'= √((6)²+ (4)²)
⇒ Distance 'd'= √(36 + 16)
⇒ Distance 'd'= √(52)
⇒ Distance 'd'= 2√13
⇒ Distance 'd'= 7.21 units.
Therefore, the distance between the points (-3,1) and (3,5) is approximately equals to 7.21 units.
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Lana draws ΔLMN on the coordinate plane. What number of units is the perimeter of ΔLMN? Round to the nearest unit.
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The calculated value of the perimeter of the triangle LMN is 25 units
Calculating the perimeter of a triangleThe formula for calculating the perimeter of triangle LMN is expressed as:
Perimeter of LMN = LM + MN + LN
From the figure
LN = 12 units
Then, we have
LM = MN = √(3-(-3))²+(5-2)²
LM = MN = √6²+3²
LM = MN = √45
LM = MN = 6.71 units
The perimeter of triangle LMN is
Perimeter = 12 units + 2(6.71) units
The perimeter of triangle LMN = 25.42 units
Hence the perimeter of the triangle( LMN) round to the nearest unit is 25 units
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Find the exact an ordinary interest for 240-day loan of $30,000 with the rate of 7% to the nearest cent. What is the difference between the 2 interest amount? Assume it is not a leap year.
a. $19.18
b. $18.19
c. $20.86
d. $17.23
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The difference between the exact and ordinary interest on the loan is $18.19. The Option B.
What is the difference between the 2 interest amount?Exact Interest:
= Principal x (1 + r)^n - Principal where n = 240 / 30 = 8 and r = 0.07 / 12 = 0.00583.
Plugging the values:
= $30,000 x (1 + 0.00583)^8 - $30,000
= $31,418.19 - $30,000
= $1,418.19
Ordinary Interest:
= Principal x Rate x Time where time = 240 / 360 = 2/3 years
Plugging the values:
= $30,000 x 0.07 x 2/3
= $1,400
The difference between Exact and Ordinary Interest:
= Exact Interest - Ordinary Interest
= $1,418.19 - $1,400
= $18.19
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Susan wants to make aprons for cooking. She needs one and three fourths yards of fabric for the front of the apron and three eighths yards of fabric for the tie. Part A: Calculate how much fabric is needed to make 3 aprons? Show every step of your work. (5 points) Part B: If Susan originally has 7 yards of fabric, how much is left over after making the aprons? Show every step of your work. (5 points) Part C: Does Susan have enough fabric left to make another apron? Explain why or why not. (2 points)
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Susan would need 6(3/8) yards of fabric.
5/8 yards of fabric are left over after making the aprons.
Susan does not have enough fabric left to make another apron
We have,
Part A:
To make one apron, Susan needs 1 3/4 + 3/8 = 2 1/8 yards of fabric.
To make 3 aprons, Susan would need 3 × 2 1/8 = 6 3/8 yards of fabric.
Part B:
Susan needs 6 3/8 yards of fabric to make 3 aprons.
If she originally had 7 yards of fabric, then the amount of fabric left after making the aprons would be:
7 - 6 3/8 = 5/8 yards of fabric.
So, 5/8 yards of fabric are left over after making the aprons.
Part C:
Susan needs 2 1/8 yards of fabric to make one apron.
She has 5/8 yards of fabric left over after making 3 aprons.
Therefore, Susan does not have enough fabric left to make another apron because 5/8 yards is less than 2 1/8 yards required to make one apron.
Thus,
Susan would need 6(3/8) yards of fabric.
5/8 yards of fabric are left over after making the aprons.
Susan does not have enough fabric left to make another apron
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What function best models the data?
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It G my teacher gave me the same question on a test ( please give me brainleist so i can rank )
Answer:
Plot the points on the graphing calculator, and then generate an exponential regression model. That model is
r(x) = 223.06(1.09^x)
The correct answer is F.
Find the slope of the line
Answers
Answer: [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
We will use the formula, or rise over run, to solve for the slope.
Formula:
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Coordinate points we will use:
(-8, 0) and (0, -4)
Substitute values and evaluate:
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]\displaystyle \frac{-4-0}{0--8}=\frac{-4}{8} =-\frac{1}{2}[/tex]
Answer: -1/2
Step-by-step explanation:
You can count the slope from the graph m=rise/run
if you started on point (-8, 0) and counted to (0,-4)
went down 4 = -4
you went right 8 = 8
m = [tex]\frac{-4}{8}[/tex] = [tex]-\frac{1}{2}[/tex]
Help me with this question
Answers
Answer:
x = 39
y = -6
Step-by-step explanation:
We are already given one of our answers which is y = -6.
Seeing our second equation, we must substitute our y-value into our second equation to find the value of x.
x= -8(-6) - 9
x = 48 - 9
x= 39
Thus, we know that the value of x is 39.
if your p-value is .11, and the significance level is .05, what do you conclude?
Answers
The p-value is .11 and the significance level is .05, then we fail to reject the null hypothesis.
The p-value represents the probability of obtaining the observed results, or results more extreme, assuming the null hypothesis is true. In this case, the p-value is greater than the significance level, which means that the observed results are not significant enough to reject the null hypothesis.
With a p-value of .11 and a significance level of .05, we can conclude that there is not enough evidence to reject the null hypothesis.
When comparing the p-value to the significance level (0.05), if the p-value is less than or equal to the significance level, you would reject the null hypothesis, indicating that there is a significant effect or difference.
If the p-value is greater than the significance level, you would fail to reject the null hypothesis, meaning that you cannot conclude that there is a significant effect or difference.
Hence, the p-value (0.11) is greater than the significance level (0.05), you fail to reject the null hypothesis, which means you cannot conclude that there is a significant effect or difference.
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A new suspension bridge is being built in Sunnydale. The last cable is being attached to the top of the tower. The cable is 400 feet long and has an a 39 degrees. Complete the sentence below to determine the height of the tower. Show your work on paper.
The tower, when rounded to the nearest foot, has a height of about……Ft
Answers
The height of the tower is about 250 feet.
We can use trigonometry to determine the height of the tower.
Let's label the height of the tower as "h". Then we can use the sine function:
sin(39) = h/400
Multiplying both sides by 400, we get:
h = 400 × sin(39)
h = 250.11.
Hence, the height of the tower is about 250 feet.
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3 pears cost $p, 1 orange costs $1.50 and 1 apple costs $2. Ms Ng bought 9 pears, 2n oranges and (n+2) apples.
(a) find in terms of p or n, the cost of
(i) 9 pears
(ii) (n+2) apples
(b) find in terms of p and n, the total cost of the fruits she bought
Answers
The total cost of the fruits she bought is 3p + 5n + 4
Find in terms of p or n, the cost of 9 pears and (n+2) applesGiven that
3 pears cost $p, 1 orange costs $1.501 apple costs $2We have
9 pears = 3 * 3 pears
So, we have
9 pears = 3 * p
9 pears = 3p
Also, we have
n + 2 apple = 2 * (n + 2)
n + 2 apple = 2n + 4
Finding in terms of p and n, the total cost of the fruits she boughtWe simply add the total of each together
So, we have
Total = 3p + 2n + 4 + 1.50 * 2n
Total = 3p + 2n + 4 + 3n
Evaluate
Total = 3p + 5n + 4
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Pls answer both questions
15) For the following scenario, make a sketch of the similar triangles, label the proportional sides, and then
solve. A fourteen-story hotel in an amusement park cast a 25-foot shadow. At the same time, a nearby 120-foot
bungee jumping tower cast a 12-foot shadow. What is the height of the hotel?
16) In the previous problem, a reasonable estimate would be to expect that the height of the building is (taller
or shorter) than the height of the tower? Please explain.
Answers
15) The height of the hotel is given as follows: 250 foot.
16) A reasonable estimate would be for the height of the building to be taller than the height of the tower, as it casts a larger shadow.
How to obtain the height of the hotel?The height of the hotel is obtained applying the proportions in the context of the problem.
The proportions are applied by a rule of three, between the height of the building and it's shadow, as follows:
x foot - 25 feet
120 foot - 12 feet
The height of the building is the height of the shadow multiplied by 10, hence the height is given as follows:
25 x 10 = 250 foot.
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Need help in bearings final answer in reasons of angles not trigonometry please, giving 40 points
Answers
Therefore, the distance of the submarine from P is approximately 1035.5 m.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the study of relationships between the sides and angles of triangles. It is particularly concerned with the measurement of angles, the computation of trigonometric functions such as sine, cosine, and tangent, and their applications to real-world problems, including engineering, physics, and astronomy. Trigonometry also includes the study of trigonometric identities and equations, as well as the use of trigonometric formulas to solve problems involving triangles and angles.
Here,
Let the distance between P and X be d and the distance between X and S be x. We are given that:
The bearing of S from P is 030°.
The bearing of S from Q is 085°.
The distance between P and Q is 1000 m.
To find x, we can use the Law of Sines, which states:
sin A / a = sin B / b = sin C / c
where A, B, and C are the angles of a triangle and a, b, and c are the lengths of the opposite sides. In our case, we have:
A = 180° - 30° = 150° (angle XPQ)
B = 180° - 85° = 95° (angle XQP)
C = 180° (angle XPS)
We also have:
a = 1000 m (PQ)
b = d (PX)
c = x (XS)
Using the Law of Sines, we can write:
sin 150° / 1000 = sin 95° / d = sin 180° / x
Solving for d, we get:
d = sin 95° / sin 150° * 1000
= 893.3 m (approx)
Solving for x, we get:
x = sin 180° / sin 150° * 893.3
= 1035.5 m (approx)
To make a scale drawing, we can choose a suitable scale, such as 1 cm = 100 m. We can then draw a line segment of length 10 cm to represent the distance between P and Q, and draw perpendiculars from P and Q to represent the bearings of the submarine. We can then use a protractor to measure the angles and draw the lines for the bearings, and measure the distance between the lines to find the distance of the submarine from P.
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Each cup. Of coffee is sold for 1. 25 and each cup of hot chocolate is sold for 0. 75 at the end of the friday wight baseball game, 170 cups of coffee and hot chocolate had been sold. Write and solve a system of equations to represent the number of cups of chocolate and coffee
Answers
The system of equations that represents the number of cups of coffee and hot chocolate sold is x + y = 170. But [tex]1.25x + 0.75y =[/tex] Total revenue.
What is the system of equations for the sales?Let x be the number of cups of coffee sold
Let y be the number of cups of hot chocolate sold.
From the problem, we know that:
The cup of coffee is sold $1.25, so, the total revenue from coffee sales is 1.25x.The cup of hot chocolate is sold $0.75, so, the total revenue from hot chocolate sales is 0.75y.The total number of cups sold is 170, so, equation for number of cups of chocolate and coffee sold will be:
x + y = 170.
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Find the equation of a line perpendicular to y - 9 = - x that passes through the point (2, 3)
Answers
The equation for the linear equation perpendicular to y - 9 = - x is:
y = x +1
How to find the equation of the perpendicular line?Two linear equations are perpendicular if the product betwen the slopes is -1.
Here we want a line perpendicular to:
y - 9 = -x
isolating y:
y = -x + 9
Then the slope is -1, thus, the slope of the perpendicular line a is:
a*-1 = -1
a = -1/-1
a = 1
Then our line is:
y = x + c
Now we want our line to pass through (2, 3), replacing these values we will get:
3 = 2 + c
3 - 2 = c
1 = c
The linear equation is:
y = x +1
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