What s 4 x 90 divided by 3 x 7?, №17886250, 21.01.2023 06:47

Mathematics

What s 4 x 90 divided by 3 x 7?

Step-by-step answer

P Answered by PhD

1

(4 × 90) ÷ (3 × 7)

= 360 ÷ 21

= 17.14

Mathematics

7.06 1. find the first six terms of the sequence. a1 = -7, an = 4 • an-1 a) -7, -28, -112, -448, -1792, -7168 b) -28, -112, -448, -1792, -7168, -28,672 c) -7, -28, -24, -20, -16, -12 d) 0, 4, -28, -24, -20, -16 2. find an equation for the nth term of the arithmetic sequence. -13, -8, -3, 2, an = -13 x 5(n - 1) an = -13 + 5(n - 1) an = -13 + 5(n + 2) an = -13 + 5(n + 1) 3. find an equation for the nth term of the arithmetic sequence. a15 = -53, a16 = -5 a) an = -725 - 48(n - 1) b) an = -725 + 48(n + 1) c) an = -725 + 48(n - 1) d) an = -725 - 48(n

Step-by-step answer

P Answered by PhD

21

1. A. According to the expression a_n=4*a_n-1, each term after a1 is four times the previous term. The first term is -7 as given, 2nd term should be -7*4=-28, 3rd term is -28*4=-112, ... A is the correct answer.

2. B. The sequence is -13, -8, -3, 2... It's obvious that each term is equal to the previous term plus 5. This is an arithmetic sequence with initial term -13 and common difference 5. We know a1=-13, so a_n=-13+5*(n-1). The answer is B.

3. A. We are given a15=-53, a16=-5. The common difference of the arithmetic sequence is -5-(-53)=48. The formula for a_n term is a1+48*(n-1). We know that a15=-13; plug in n=15, a15=-53=a1+48*(15-1), a1=-725. So a_n=-725+48*(n-1).

4. Diverge. We are given a few terms, 11, 44, 176, 704... Observe that each term is four times the previous one. 11*4=44, 44*4=176, 176*4=704... This is a geometric series with common ratio>1. You can keep multiplying by 4 and the series goes to infinity, so it diverges.

5. D. We have -4, -16, -64, -256... Same as above, each term is four times the previous one. The initial term is a1=-4. The common ratio d=4. So a_n=a1*d^(n-1)=-4*4^(n-1)=-4^n. (D).

6. The answer is A. a2=-2, a5=16. Suppose the common ratio is D. a_n=a1*d^(n-1). a2=a1*d; a5=a1*d^4. Plug in a2 and a5: -2=a1*d, 16=a1*d^4. 16/-2=d^3=-8, d=-2, a1=1. So a_n=1*(-2)^(n-1).

7. B. We are given the sequence 4, -24, 144,... Each term is -6 times the previous one. The first term a0=4, the n^th term a_(n-1) is a1*d^n=4*(-6)^n. To express the sum, we simply have to use the sigma notation and sum 4*(-6)^n from n=0 to infinity. The answer is B.

8. D. We are given -3 + 6 + 15 + 24... 132. Each term is equal to the previous one plus 9. First term a0=-3, n^th term a_n-1 is -3+9*n. The last term is 132. 132 =-3+9n, n=15. So we have to sum -3+9n from n=0 to n=15.

9. B. 343 + 512 + 729 + 1000+... 343=7^3, 512=8^3, 729=9^3, 1000=10^3. This is a sequence of perfect cubes. Therefore, the sum is n^3 from n=7 to infinity. (The initial term is 343=7^3).

10. B. We are given 3, 5, 7, 9, ... 21. The common difference is 2. There are (21-3)/2+1=10 terms. The initial term a1=3, and last term is a10=21. The sum is (a1+a10)*10/2=(3+21)*10/2=120.

11. C. 4/3, 16/3, 64/3, 256/3, 1024/3. Each term is four times the previous one. This is a geometric series with initial term a1=4/3 and common ratio r=4. 1024/3 is the 5th term of the sequence. So sum=a1*(1-r^n)/(1-r)=4/3*(1-4^5)/(1-4)=-4/9*-1023=1364/3.

12. B. 10,12,14,... This is an arithmetic sequence. a1=10, and common difference d=2. There are 20 terms (20 rows). a20=a1+d*(n-1)=10+2*(20-1)=48. So the sum S=(a1+an)*n/2=(10+48)*20/2=580.

13. 10 + 20 + 30 + ... + 10n = 5n(n + 1). When n=1, this expression is true, since 10=5*1*(1+1). Suppose when n=k, this statement is true, then when n=k+1, the left side is 10+...+10n+10(n+1), the right side is 5(n+1)(n+2). The left side adds 10(n+1) compared to the previous one. The right side adds 5(n+1)(n+2)-5n(n+1)=5(n+1)(n+2-n)=10(n+1). So the statement holds true.

14. The height at week 0 is a0=300 (initial height). Common difference is 4.2 (weekly increment). a_n=300+4.2n. At week n, the height of the tree is 300+4.2*n centimeters.

Mathematics

7.06 1. find the first six terms of the sequence. a1 = -7, an = 4 • an-1 a) -7, -28, -112, -448, -1792, -7168 b) -28, -112, -448, -1792, -7168, -28,672 c) -7, -28, -24, -20, -16, -12 d) 0, 4, -28, -24, -20, -16 2. find an equation for the nth term of the arithmetic sequence. -13, -8, -3, 2, an = -13 x 5(n - 1) an = -13 + 5(n - 1) an = -13 + 5(n + 2) an = -13 + 5(n + 1) 3. find an equation for the nth term of the arithmetic sequence. a15 = -53, a16 = -5 a) an = -725 - 48(n - 1) b) an = -725 + 48(n + 1) c) an = -725 + 48(n - 1) d) an = -725 - 48(n

Step-by-step answer

P Answered by PhD

21

1. A. According to the expression a_n=4*a_n-1, each term after a1 is four times the previous term. The first term is -7 as given, 2nd term should be -7*4=-28, 3rd term is -28*4=-112, ... A is the correct answer.

2. B. The sequence is -13, -8, -3, 2... It's obvious that each term is equal to the previous term plus 5. This is an arithmetic sequence with initial term -13 and common difference 5. We know a1=-13, so a_n=-13+5*(n-1). The answer is B.

3. A. We are given a15=-53, a16=-5. The common difference of the arithmetic sequence is -5-(-53)=48. The formula for a_n term is a1+48*(n-1). We know that a15=-13; plug in n=15, a15=-53=a1+48*(15-1), a1=-725. So a_n=-725+48*(n-1).

4. Diverge. We are given a few terms, 11, 44, 176, 704... Observe that each term is four times the previous one. 11*4=44, 44*4=176, 176*4=704... This is a geometric series with common ratio>1. You can keep multiplying by 4 and the series goes to infinity, so it diverges.

5. D. We have -4, -16, -64, -256... Same as above, each term is four times the previous one. The initial term is a1=-4. The common ratio d=4. So a_n=a1*d^(n-1)=-4*4^(n-1)=-4^n. (D).

6. The answer is A. a2=-2, a5=16. Suppose the common ratio is D. a_n=a1*d^(n-1). a2=a1*d; a5=a1*d^4. Plug in a2 and a5: -2=a1*d, 16=a1*d^4. 16/-2=d^3=-8, d=-2, a1=1. So a_n=1*(-2)^(n-1).

7. B. We are given the sequence 4, -24, 144,... Each term is -6 times the previous one. The first term a0=4, the n^th term a_(n-1) is a1*d^n=4*(-6)^n. To express the sum, we simply have to use the sigma notation and sum 4*(-6)^n from n=0 to infinity. The answer is B.

8. D. We are given -3 + 6 + 15 + 24... 132. Each term is equal to the previous one plus 9. First term a0=-3, n^th term a_n-1 is -3+9*n. The last term is 132. 132 =-3+9n, n=15. So we have to sum -3+9n from n=0 to n=15.

9. B. 343 + 512 + 729 + 1000+... 343=7^3, 512=8^3, 729=9^3, 1000=10^3. This is a sequence of perfect cubes. Therefore, the sum is n^3 from n=7 to infinity. (The initial term is 343=7^3).

10. B. We are given 3, 5, 7, 9, ... 21. The common difference is 2. There are (21-3)/2+1=10 terms. The initial term a1=3, and last term is a10=21. The sum is (a1+a10)*10/2=(3+21)*10/2=120.

11. C. 4/3, 16/3, 64/3, 256/3, 1024/3. Each term is four times the previous one. This is a geometric series with initial term a1=4/3 and common ratio r=4. 1024/3 is the 5th term of the sequence. So sum=a1*(1-r^n)/(1-r)=4/3*(1-4^5)/(1-4)=-4/9*-1023=1364/3.

12. B. 10,12,14,... This is an arithmetic sequence. a1=10, and common difference d=2. There are 20 terms (20 rows). a20=a1+d*(n-1)=10+2*(20-1)=48. So the sum S=(a1+an)*n/2=(10+48)*20/2=580.

13. 10 + 20 + 30 + ... + 10n = 5n(n + 1). When n=1, this expression is true, since 10=5*1*(1+1). Suppose when n=k, this statement is true, then when n=k+1, the left side is 10+...+10n+10(n+1), the right side is 5(n+1)(n+2). The left side adds 10(n+1) compared to the previous one. The right side adds 5(n+1)(n+2)-5n(n+1)=5(n+1)(n+2-n)=10(n+1). So the statement holds true.

14. The height at week 0 is a0=300 (initial height). Common difference is 4.2 (weekly increment). a_n=300+4.2n. At week n, the height of the tree is 300+4.2*n centimeters.

SAT

The following data is on X=Automobile Stock per capita, P= Relative price of automobiles and Id= Real disposable income per capita Years Xt Pt Idt Years Xt Pt Idt 1921 4.8 120.9 407.8 1937 8.34 100 551.2 1922 5.42 111.2 460.4 1938 7.78 109.3 511 1923 6.88 100.6 509.2 1939 7.72 104.9 547.9 1924 7.84 90.9 509.3 1940 8.22 97.1 578.8 1925 8.41 81.7 525.6 1941 9.17 120.1 642.7 1926 8.93 92.6 532.3 1942 7.42 119 719.1 1927 8.77 105.6 543.3 1943 5.79 204.7 741.6 1928 9.13 91 545.1 1944 4.45 356.7 798 1929 9.69 95.1 576.2 1945 3.51 449.3 787.2 1930 9.09

Step-by-step answer

P Answered by Master

gamsahabnida gamsahabnida

The following data is on

X=Automobile Stock per capita,P= Relative price of automobiles andId= Rea

Mathematics

If you answer this you are my hero and good things will happen to you. which is bigger: or 0.78? 6.6 11. if x = 2, calculate the value of: x2 - x 21. work out the height of a parallelogram of base 10m and area 60m2. 6.2 2. decrease £900 by 5% 6.7 12. solve: 2(x + 3) = 8 6.3 3. divide £360 in a ratio of 1: 4 6.8 13. find the nth term of this sequence 3 8 13 18 23 22. three of the angles of a quadrilateral are 1320, 140 and 1050. what is the size of the 4th angle? 6.4 4. if 75% is £66, what is the full cost? 6.9 14. if y=4x - 1, find the value of

Step-by-step answer

P Answered by PhD

17

Which is bigger 6.6 or 0.78 ?
6.6 is bigger

x^2 - xwhen x = 2
2^2 - 2 =
4 - 2 =
2 <==

A = bh
60 = 10h
60/10 = h
6 = hso height is 6 m

900 decreased by 5% =
900 - 0.05(900) = 900 - 45 = 855 <==

2(x + 3) = 8
2x + 6 = 8
2x = 8 - 6
2x = 2
x = 2/2
x = 1 <==

360 in a ratio of 1 to 4

1:4added = 5

1/5(360) = 360/5 = 72
4/5(360) = 1440/5 = 288

ratio is 72:288

3,8,13,16,23this is an arithmetic sequence with a common difference of 5

the nth term : an = a1 + (n - 1)d
an = 3 + 5(n-1) <===

are there decimals in this problembecause the angles of a quadrilateral , when added = 360 degrees

75% = 66what is full cost...
75% of what is 66..
0.75x = 66
x = 66 / 0.75
x = 88 <==

y = 4x - 1...when x = -2
y = 4(-2) - 1
y = -8 - 1
y = -9 <==

6.5 cant see the problem

circumference of circle with radius of 4
C = 2(pi)r
C = 2(3.14)(4)
C = 25.12 cm <== or C = 8*(pi)

6 km / h for 2 hrs 20 min...

6 / 60 = 0.1 km per minute0.1(140) = 14 km <==

to increase an amount by 4.6%, ur multiplier would be 1.046

(x - 5)(x + 4) =
x^2 + 4x - 5x - 20 =
x^2 - x - 20 <===

500 increased by 4.6%
500(1.046) = 523 <==

2x > 7
x > 7/2 or x > 3.5

500 tickets are soldprobability of winning first prize (if there is only 1 first prize) is 1/500dont know how many tickets he bought

6 * 0.6 = 3.6u simply multiply 6 * 6 = 36and since 0.6 has a decimal 1 space to the left, in ur answer(36)...move the decimal 1 space to the left giving u 3.6

5x - 2ywhen x = -2, y = -3
5(-2) - 2(-3) =
-10 + 6 =
-4 <==

0.521 to one significant figure = 0.5

4,7,13,22,34
4 to 7 = 3 spaces
7 to 13 = 5 spaces
13 to 22 = 9 spaces
22 to 34 = 12 spaces
I am sorryI do not know this one..cannot find the pattern

V= bh
V = 3*10
V = 30
not sure about this...because volume of a prism is base * heightthere is o (pi) in the formula.

7.34 * 4.71 = 34.5714 rounds to 34.57
5.63 + 11.89 = 17.52

y = x^2 + 2xx = -2
y = -2^2 + 2(-2)
y = 4 - 4
y = 0 <==

Mathematics

If you answer this you are my hero and good things will happen to you. which is bigger: or 0.78? 6.6 11. if x = 2, calculate the value of: x2 - x 21. work out the height of a parallelogram of base 10m and area 60m2. 6.2 2. decrease £900 by 5% 6.7 12. solve: 2(x + 3) = 8 6.3 3. divide £360 in a ratio of 1: 4 6.8 13. find the nth term of this sequence 3 8 13 18 23 22. three of the angles of a quadrilateral are 1320, 140 and 1050. what is the size of the 4th angle? 6.4 4. if 75% is £66, what is the full cost? 6.9 14. if y=4x - 1, find the value of

Step-by-step answer

P Answered by PhD

17

Which is bigger 6.6 or 0.78 ?
6.6 is bigger

x^2 - xwhen x = 2
2^2 - 2 =
4 - 2 =
2 <==

A = bh
60 = 10h
60/10 = h
6 = hso height is 6 m

900 decreased by 5% =
900 - 0.05(900) = 900 - 45 = 855 <==

2(x + 3) = 8
2x + 6 = 8
2x = 8 - 6
2x = 2
x = 2/2
x = 1 <==

360 in a ratio of 1 to 4

1:4added = 5

1/5(360) = 360/5 = 72
4/5(360) = 1440/5 = 288

ratio is 72:288

3,8,13,16,23this is an arithmetic sequence with a common difference of 5

the nth term : an = a1 + (n - 1)d
an = 3 + 5(n-1) <===

are there decimals in this problembecause the angles of a quadrilateral , when added = 360 degrees

75% = 66what is full cost...
75% of what is 66..
0.75x = 66
x = 66 / 0.75
x = 88 <==

y = 4x - 1...when x = -2
y = 4(-2) - 1
y = -8 - 1
y = -9 <==

6.5 cant see the problem

circumference of circle with radius of 4
C = 2(pi)r
C = 2(3.14)(4)
C = 25.12 cm <== or C = 8*(pi)

6 km / h for 2 hrs 20 min...

6 / 60 = 0.1 km per minute0.1(140) = 14 km <==

to increase an amount by 4.6%, ur multiplier would be 1.046

(x - 5)(x + 4) =
x^2 + 4x - 5x - 20 =
x^2 - x - 20 <===

500 increased by 4.6%
500(1.046) = 523 <==

2x > 7
x > 7/2 or x > 3.5

500 tickets are soldprobability of winning first prize (if there is only 1 first prize) is 1/500dont know how many tickets he bought

6 * 0.6 = 3.6u simply multiply 6 * 6 = 36and since 0.6 has a decimal 1 space to the left, in ur answer(36)...move the decimal 1 space to the left giving u 3.6

5x - 2ywhen x = -2, y = -3
5(-2) - 2(-3) =
-10 + 6 =
-4 <==

0.521 to one significant figure = 0.5

4,7,13,22,34
4 to 7 = 3 spaces
7 to 13 = 5 spaces
13 to 22 = 9 spaces
22 to 34 = 12 spaces
I am sorryI do not know this one..cannot find the pattern

V= bh
V = 3*10
V = 30
not sure about this...because volume of a prism is base * heightthere is o (pi) in the formula.

7.34 * 4.71 = 34.5714 rounds to 34.57
5.63 + 11.89 = 17.52

y = x^2 + 2xx = -2
y = -2^2 + 2(-2)
y = 4 - 4
y = 0 <==

Mathematics

1. product of 5r and 7 divided by 15 2. 120% of the sum of w and one-twelfth u 3. 20% of one half w 4. sum of x, three-fourths x, and 90% of z. 5. four times the difference of one-half x subtracted from three-eighths y. 6. 60% of the difference of five-eighteenths v subtracted from four-sixths w.

Step-by-step answer

P Answered by Specialist

10

1) 5r*7/15 = 35r/15 = 7r/3
2) 1.2 (w + u/12) = 1.2w + 0.1u
3) 0.2w/2 = 0.1w
4) x +3x/4 + 0.9z = 1.75x + 0.9z
5) 4*( 3y/8 - x/2) = 1.5y -2x
6) 0.6* ( 4w/6 - 5v/18 ) = 2w/5 - 5v/3

Mathematics

1. product of 5r and 7 divided by 15 2. 120% of the sum of w and one-twelfth u 3. 20% of one half w 4. sum of x, three-fourths x, and 90% of z. 5. four times the difference of one-half x subtracted from three-eighths y. 6. 60% of the difference of five-eighteenths v subtracted from four-sixths w.

Step-by-step answer

P Answered by Specialist

10

1) 5r*7/15 = 35r/15 = 7r/3
2) 1.2 (w + u/12) = 1.2w + 0.1u
3) 0.2w/2 = 0.1w
4) x +3x/4 + 0.9z = 1.75x + 0.9z
5) 4*( 3y/8 - x/2) = 1.5y -2x
6) 0.6* ( 4w/6 - 5v/18 ) = 2w/5 - 5v/3

Mathematics

Aparabola has a focus of f(2,8.5) and a directrix of y=9.5. the point p(x,y) represents any point on the parabola, while d(x,9.5) represents any point on the directrix. maria was asked to use the distance formula to write an equation to represent this parabola. here is her work: step 1: fp=dp step 2: (x−2)2+(y−8.5)2−−−−−−−−−−−−−−−−√=(x−x)2+(y−9.5)2−−−−−−−−−−−−−−−−−√ step 3: x2−4x+4+y2−17y+72.25=y2−19y+90.25 step 4: x2−4x−14=−4y step 5: −14x2+x+72=y identify each incorrect step. select all answer choices that both state an incorrect step and explain

Step-by-step answer

P Answered by Specialist

1

(4)and (7)

Step-by-step explanation:

A parabola has a focus of F(2,8.5) and a directrix of y=9.5. The point P(x,y) represents any point on the parabola, while D(x,9.5) represents any point on the directrix.

Now, Step 1: FP=DP, using the distance formula,

Step 2: $\sqrt{(y-8.5)^{2}+(x-2)^{2}}=\sqrt{(y-9.5)^{2}+(x-x)^{2}}$

Step 3: Solving the step 2,we get

$\sqrt{(y-8.5)^{2}+(x-2)^{2}}=\sqrt{(y-9.5)^{2} }$

Squaring on both sides and then solving, we get

$x^{2}-4x+4+y^{2}-17y+72.25=y^{2}-19y+90.25$

Step 4: $x^{2}-4x-14=-2y$

Step 5: Finding the value of y by dividing both sides by -2, we get

$\frac{x^{2}-4x-14}{-2}=y$

Thus, Step 4 and 5 is incorrect because she added the y-terms incorrectly and also the previous step is incorrect on step 4.

Mathematics

Aparabola has a focus of f(2,8.5) and a directrix of y=9.5. the point p(x,y) represents any point on the parabola, while d(x,9.5) represents any point on the directrix. maria was asked to use the distance formula to write an equation to represent this parabola. here is her work: step 1: fp=dp step 2: (x−2)2+(y−8.5)2−−−−−−−−−−−−−−−−√=(x−x)2+(y−9.5)2−−−−−−−−−−−−−−−−−√ step 3: x2−4x+4+y2−17y+72.25=y2−19y+90.25 step 4: x2−4x−14=−4y step 5: −14x2+x+72=y identify each incorrect step. select all answer choices that both state an incorrect step and explain

Step-by-step answer

P Answered by Specialist

1

(4)and (7)

Step-by-step explanation:

A parabola has a focus of F(2,8.5) and a directrix of y=9.5. The point P(x,y) represents any point on the parabola, while D(x,9.5) represents any point on the directrix.

Now, Step 1: FP=DP, using the distance formula,

Step 2: $\sqrt{(y-8.5)^{2}+(x-2)^{2}}=\sqrt{(y-9.5)^{2}+(x-x)^{2}}$

Step 3: Solving the step 2,we get

$\sqrt{(y-8.5)^{2}+(x-2)^{2}}=\sqrt{(y-9.5)^{2} }$

Squaring on both sides and then solving, we get

$x^{2}-4x+4+y^{2}-17y+72.25=y^{2}-19y+90.25$

Step 4: $x^{2}-4x-14=-2y$

Step 5: Finding the value of y by dividing both sides by -2, we get

$\frac{x^{2}-4x-14}{-2}=y$

Thus, Step 4 and 5 is incorrect because she added the y-terms incorrectly and also the previous step is incorrect on step 4.

What's 4 x 90 divided by 3 x 7?

Step-by-step answer

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